Làm thế nào để bạn viết loại bỏ gaussian trong python?

Bài viết tập trung vào việc sử dụng thuật toán giải hệ phương trình tuyến tính. Chúng ta sẽ đối phó với ma trận các hệ số. Loại bỏ Gaussian không hoạt động trên các ma trận đơn lẻ (chúng dẫn đến chia cho 0)

Nội dung chính Show

Ví dụ loại bỏ Gaussian là gì?
Loại bỏ Gaussian là ref hay rref?
Thuật toán loại bỏ Gaussian là gì?

Input: For N unknowns, input is an augmented 
       matrix of size N x (N+1). One extra 
       column is for Right Hand Side (RHS)
  mat[N][N+1] = {{3.0, 2.0,-4.0, 3.0},
                {2.0, 3.0, 3.0, 15.0},
                {5.0, -3, 1.0, 14.0}
               };
Output: Solution to equations is:
        3.000000
        1.000000
        2.000000

Explanation:
Given matrix represents following equations
3.0X1 + 2.0X2 - 4.0X3 =  3.0
2.0X1 + 3.0X2 + 3.0X3 = 15.0
5.0X1 - 3.0X2 +    X3 = 14.0

There is a unique solution for given equations, 
solutions is, X1 = 3.0, X2 = 1.0, X3 = 2.0,

Hình thức cấp bậc hàng. Ma trận được cho là trong r. e. f. nếu các điều kiện sau giữ.

Phần tử khác không đầu tiên trong mỗi hàng, được gọi là hệ số hàng đầu, là 1
Mỗi hệ số hàng đầu nằm trong một cột ở bên phải của hàng trước hệ số hàng đầu
Các hàng có tất cả các số 0 nằm bên dưới các hàng có ít nhất một phần tử khác 0

Giảm hình thức cấp bậc hàng. Ma trận được cho là trong r. r. e. f. nếu các điều kiện sau giữ -

Tất cả các điều kiện cho r. e. f
Hệ số hàng đầu trong mỗi hàng là mục nhập khác 0 duy nhất trong cột của nó

Thuật toán chủ yếu là thực hiện một chuỗi các thao tác trên các hàng của ma trận. Điều chúng tôi muốn lưu ý khi thực hiện các thao tác này là chúng tôi muốn chuyển đổi ma trận thành ma trận tam giác trên ở dạng cấp bậc hàng. Các hoạt động có thể được.

Hoán đổi hai hàng
Nhân một hàng với một vô hướng khác không
Thêm vào một hàng một bội số của một hàng khác

Quá trình.

Chuyển tiếp loại bỏ. giảm xuống dạng cấp bậc. Sử dụng nó, người ta có thể biết liệu không có giải pháp, hoặc giải pháp duy nhất hoặc vô số giải pháp
Sự thay thế sau. tiếp tục giảm xuống dạng cấp bậc giảm

thuật toán.

xoay một phần. Tìm trục thứ k bằng cách hoán đổi các hàng, để di chuyển mục nhập có giá trị tuyệt đối lớn nhất đến vị trí trục. Điều này truyền đạt tính ổn định tính toán cho thuật toán
Đối với mỗi hàng bên dưới trục, hãy tính hệ số f làm cho mục nhập thứ k bằng 0 và đối với mỗi phần tử trong hàng trừ bội số thứ f của phần tử tương ứng trong hàng thứ k
Lặp lại các bước trên cho từng ẩn số. Chúng tôi sẽ để lại một phần r. e. f. ma trận

Dưới đây là việc thực hiện các thuật toán trên.

C++

// C++ program to demonstrate working of Gaussian Elimination

// method

#include<bits/stdc++.h>

using namespace std;

#define N 3 // Number of unknowns

// function to reduce matrix to r.e.f. Returns a value to

Solution for the system:
3.000000
1.000000
2.000000

Solution for the system:
3.000000
1.000000
2.000000

Solution for the system:
3.000000
1.000000
2.000000

Solution for the system:
3.000000
1.000000
2.000000

Solution for the system:
3.000000
1.000000
2.000000

Solution for the system:
3.000000
1.000000
2.000000

Solution for the system:
3.000000
1.000000
2.000000

Solution for the system:
3.000000
1.000000
2.000000

7_______1_______3

Solution for the system:
3.000000
1.000000
2.000000

// C++ program to demonstrate working of Gaussian Elimination0

Solution for the system:
3.000000
1.000000
2.000000

6 // C++ program to demonstrate working of Gaussian Elimination2

Solution for the system:
3.000000
1.000000
2.000000

3 // C++ program to demonstrate working of Gaussian Elimination4

// C++ program to demonstrate working of Gaussian Elimination5

// C++ program to demonstrate working of Gaussian Elimination6_______554_______7

// C++ program to demonstrate working of Gaussian Elimination6______1_______1 // method0

// C++ program to demonstrate working of Gaussian Elimination6_______555_______2

// C++ program to demonstrate working of Gaussian Elimination6_______555_______4 // method5

// C++ program to demonstrate working of Gaussian Elimination6_______554_______5

// method8// method9#include<bits/stdc++.h>0#include<bits/stdc++.h>1#include<bits/stdc++.h>2

// method8#include<bits/stdc++.h>4

#include<bits/stdc++.h>5____556_______6

#include<bits/stdc++.h>5____556_______8

// method8// method4 using1

using2// method9#include<bits/stdc++.h>0using5#include<bits/stdc++.h>2

// method8using8

using2// method9#include<bits/stdc++.h>0namespace2

namespace3_______558_______4#include<bits/stdc++.h>2

// method8____558_______7namespace8

// C++ program to demonstrate working of Gaussian Elimination6_______559_______0

// C++ program to demonstrate working of Gaussian Elimination6_______559_______2

std;3____559_______4

// C++ program to demonstrate working of Gaussian Elimination6_______559_______6

std;0

std;8

Solution for the system:
3.000000
1.000000
2.000000

6 #define N 3 // Number of unknowns0

Solution for the system:
3.000000
1.000000
2.000000

3 #define N 3 // Number of unknowns2

Solution for the system:
3.000000
1.000000
2.000000

1 #define N 3 // Number of unknowns4

Solution for the system:
3.000000
1.000000
2.000000

1 #define N 3 // Number of unknowns6

// C++ program to demonstrate working of Gaussian Elimination5

// C++ program to demonstrate working of Gaussian Elimination6_______560_______9

// C++ program to demonstrate working of Gaussian Elimination6_______561_______1 #include<bits/stdc++.h>0

Solution for the system:
3.000000
1.000000
2.000000

1 // function to reduce matrix to r.e.f. Returns a value to4

// C++ program to demonstrate working of Gaussian Elimination6_______554_______5

// method8____1_______3 // function to reduce matrix to r.e.f. Returns a value to9

// method8

Solution for the system:
3.000000
1.000000
2.000000

// method8

Solution for the system:
3.000000
1.000000
2.000000

// C++ program to demonstrate working of Gaussian Elimination6_______559_______0

std;0

Solution for the system:
3.000000
1.000000
2.000000

Solution for the system:
3.000000
1.000000
2.000000

Solution for the system:
3.000000
1.000000
2.000000

09_______1_______3 // C++ program to demonstrate working of Gaussian Elimination4

// C++ program to demonstrate working of Gaussian Elimination5

// C++ program to demonstrate working of Gaussian Elimination6_______561_______1 #include<bits/stdc++.h>0

Solution for the system:
3.000000
1.000000
2.000000

Solution for the system:
3.000000
1.000000
2.000000

17// method9#include<bits/stdc++.h>0

Solution for the system:
3.000000
1.000000
2.000000

Solution for the system:
3.000000
1.000000
2.000000

// method8// function to reduce matrix to r.e.f. Returns a value to1 #include<bits/stdc++.h>0

Solution for the system:
3.000000
1.000000
2.000000

Solution for the system:
3.000000
1.000000
2.000000

using2// method9#include<bits/stdc++.h>0

Solution for the system:
3.000000
1.000000
2.000000

Solution for the system:
3.000000
1.000000
2.000000

// C++ program to demonstrate working of Gaussian Elimination6_______555_______9#include<bits/stdc++.h>0

Solution for the system:
3.000000
1.000000
2.000000

20#include<bits/stdc++.h>2

std;0

Solution for the system:
3.000000
1.000000
2.000000

Solution for the system:
3.000000
1.000000
2.000000

Solution for the system:
3.000000
1.000000
2.000000

Solution for the system:
3.000000
1.000000
2.000000

3 // C++ program to demonstrate working of Gaussian Elimination4

// C++ program to demonstrate working of Gaussian Elimination5

// C++ program to demonstrate working of Gaussian Elimination6_______561_______1 #include<bits/stdc++.h>0

Solution for the system:
3.000000
1.000000
2.000000

Solution for the system:
3.000000
1.000000
2.000000

// C++ program to demonstrate working of Gaussian Elimination6_______554_______5

// method8

Solution for the system:
3.000000
1.000000
2.000000

// method8

Solution for the system:
3.000000
1.000000
2.000000

Solution for the system:
3.000000
1.000000
2.000000

// method8

Solution for the system:
3.000000
1.000000
2.000000

Solution for the system:
3.000000
1.000000
2.000000

// method8

Solution for the system:
3.000000
1.000000
2.000000

// method8// function to reduce matrix to r.e.f. Returns a value to1 #include<bits/stdc++.h>0

Solution for the system:
3.000000
1.000000
2.000000

Solution for the system:
3.000000
1.000000
2.000000

using2____555_______4 #include<bits/stdc++.h>0

Solution for the system:
3.000000
1.000000
2.000000

Solution for the system:
3.000000
1.000000
2.000000

Solution for the system:
3.000000
1.000000
2.000000

71______1_______72

// method8

Solution for the system:
3.000000
1.000000
2.000000

Solution for the system:
3.000000
1.000000
2.000000

Solution for the system:
3.000000
1.000000
2.000000

Solution for the system:
3.000000
1.000000
2.000000

Solution for the system:
3.000000
1.000000
2.000000

// method8____555_______4

Solution for the system:
3.000000
1.000000
2.000000

using2____558_______7

Solution for the system:
3.000000
1.000000
2.000000

Solution for the system:
3.000000
1.000000
2.000000

// method8

Solution for the system:
3.000000
1.000000
2.000000

// method8// method4

Solution for the system:
3.000000
1.000000
2.000000

using2

Solution for the system:
3.000000
1.000000
2.000000

// method8// function to reduce matrix to r.e.f. Returns a value to1 #include<bits/stdc++.h>0

Solution for the system:
3.000000
1.000000
2.000000

Solution for the system:
3.000000
1.000000
2.000000

// method8____554_______5

using2____554_______01

// C++ program to demonstrate working of Gaussian Elimination02____554_______03

using2

Solution for the system:
3.000000
1.000000
2.000000

3 // C++ program to demonstrate working of Gaussian Elimination06

using2____554_______08

// C++ program to demonstrate working of Gaussian Elimination09____554_______10

using2// function to reduce matrix to r.e.f. Returns a value to1 #include<bits/stdc++.h>0

Solution for the system:
3.000000
1.000000
2.000000

1 // C++ program to demonstrate working of Gaussian Elimination15

Solution for the system:
3.000000
1.000000
2.000000

71____554_______17

using2____554_______19

using2____554_______21

// method8____559_______0

// method8____554_______25

// C++ program to demonstrate working of Gaussian Elimination6_______559_______0

// C++ program to demonstrate working of Gaussian Elimination6_______554_______29

// C++ program to demonstrate working of Gaussian Elimination6_______558_______7 // C++ program to demonstrate working of Gaussian Elimination32

std;0

Solution for the system:
3.000000
1.000000
2.000000

Solution for the system:
3.000000
1.000000
2.000000

Solution for the system:
3.000000
1.000000
2.000000

7_______1_______3 // C++ program to demonstrate working of Gaussian Elimination4

// C++ program to demonstrate working of Gaussian Elimination5

// C++ program to demonstrate working of Gaussian Elimination6_______1_______3 // C++ program to demonstrate working of Gaussian Elimination42// C++ program to demonstrate working of Gaussian Elimination43

// C++ program to demonstrate working of Gaussian Elimination6_______554_______45

std;3____554_______47

// C++ program to demonstrate working of Gaussian Elimination6_______561_______1 #include<bits/stdc++.h>0

Solution for the system:
3.000000
1.000000
2.000000

1 // C++ program to demonstrate working of Gaussian Elimination52

// C++ program to demonstrate working of Gaussian Elimination6_______554_______5

// method8____554_______56

// method8____554_______58

// method8____554_______60

#include<bits/stdc++.h>5____554_______62

// method8// function to reduce matrix to r.e.f. Returns a value to1 #include<bits/stdc++.h>0

Solution for the system:
3.000000
1.000000
2.000000

1 // C++ program to demonstrate working of Gaussian Elimination67

// method8____554_______5

using2____554_______71

// C++ program to demonstrate working of Gaussian Elimination02____554_______73

// C++ program to demonstrate working of Gaussian Elimination02____554_______75

using2____554_______77

// method8____559_______0

// method8____554_______81

#include<bits/stdc++.h>5____554_______83

// method8// C++ program to demonstrate working of Gaussian Elimination85

// C++ program to demonstrate working of Gaussian Elimination6_______559_______0

// C++ program to demonstrate working of Gaussian Elimination6_______555_______9#include<bits/stdc++.h>0// C++ program to demonstrate working of Gaussian Elimination91#include<bits/stdc++.h>2

// C++ program to demonstrate working of Gaussian Elimination6_______561_______1 #include<bits/stdc++.h>0

Solution for the system:
3.000000
1.000000
2.000000

1 // C++ program to demonstrate working of Gaussian Elimination97

// method8// method9#include<bits/stdc++.h>0// method01// method02

std;0

// method04

Solution for the system:
3.000000
1.000000
2.000000

1 // method06

// C++ program to demonstrate working of Gaussian Elimination5

// C++ program to demonstrate working of Gaussian Elimination6_______555_______09

// C++ program to demonstrate working of Gaussian Elimination6______1_______3 // method12

// method13_______555_______14

// method13_______555_______16

// method17_______555_______18

// C++ program to demonstrate working of Gaussian Elimination6_______555_______20

// C++ program to demonstrate working of Gaussian Elimination6_______558_______7 // method23

std;0

Java

// method25

// method

// method27 // method28

// method29 // method30

// C++ program to demonstrate working of Gaussian Elimination5

// method32_______555_______33 // method34

Solution for the system:
3.000000
1.000000
2.000000

1 // method36// method37namespace8// method39

// method32_______554_______0

// method32_______555_______34

Solution for the system:
3.000000
1.000000
2.000000

6 // C++ program to demonstrate working of Gaussian Elimination2

Solution for the system:
3.000000
1.000000
2.000000

3 // method47

// method32_______554_______5

// C++ program to demonstrate working of Gaussian Elimination6_______554_______7

// C++ program to demonstrate working of Gaussian Elimination6______1_______1 // method0

// C++ program to demonstrate working of Gaussian Elimination6_______555_______2

// C++ program to demonstrate working of Gaussian Elimination6_______555_______4 // method59// method60// method61

// C++ program to demonstrate working of Gaussian Elimination6_______554_______5

// method64____555_______65// method66_______556_______2

// method64____556_______4

// C++ program to demonstrate working of Gaussian Elimination09____556_______6

// C++ program to demonstrate working of Gaussian Elimination09____556_______8

// method64____555_______4 // method76// method77// method61

// method8// method80using5#include<bits/stdc++.h>2

// method64____557_______8

// method8____555_______80

// method8____555_______88#include<bits/stdc++.h>2

// method64____558_______7namespace8

// C++ program to demonstrate working of Gaussian Elimination6_______559_______0

// C++ program to demonstrate working of Gaussian Elimination6_______559_______2

#include<bits/stdc++.h>5____559_______4

// C++ program to demonstrate working of Gaussian Elimination6_______559_______6

// method32_______559_______0

// method32_______556_______04

// method32_______556_______06

// method32_______555_______34

Solution for the system:
3.000000
1.000000
2.000000

6 #define N 3 // Number of unknowns0

Solution for the system:
3.000000
1.000000
2.000000

3 #include<bits/stdc++.h>12

Solution for the system:
3.000000
1.000000
2.000000

1 #define N 3 // Number of unknowns4

Solution for the system:
3.000000
1.000000
2.000000

1 #define N 3 // Number of unknowns6

// method32_______554_______5

// C++ program to demonstrate working of Gaussian Elimination6_______556_______20

// C++ program to demonstrate working of Gaussian Elimination6_______561_______1 #include<bits/stdc++.h>0

Solution for the system:
3.000000
1.000000
2.000000

1 #include<bits/stdc++.h>25// method77#include<bits/stdc++.h>27

// C++ program to demonstrate working of Gaussian Elimination6_______554_______5

// method64____1_______3 // function to reduce matrix to r.e.f. Returns a value to9

// method64____1_______01

// method64____1_______03

// C++ program to demonstrate working of Gaussian Elimination6_______559_______0

// method32_______559_______0

// method32____1_______07

// method32_______555_______34

Solution for the system:
3.000000
1.000000
2.000000

Solution for the system:
3.000000
1.000000
2.000000

Solution for the system:
3.000000
1.000000
2.000000

3 // method47

// method32_______554_______5

// C++ program to demonstrate working of Gaussian Elimination6_______561_______1 #include<bits/stdc++.h>0

Solution for the system:
3.000000
1.000000
2.000000

1 #include<bits/stdc++.h>55// method77#include<bits/stdc++.h>57

// method64// function to reduce matrix to r.e.f. Returns a value to1 #include<bits/stdc++.h>0

Solution for the system:
3.000000
1.000000
2.000000

1 #include<bits/stdc++.h>62// method77#include<bits/stdc++.h>64

// method8____556_______66

// C++ program to demonstrate working of Gaussian Elimination6_______556_______68

// method32_______559_______0

// method32____1_______38

// method32_______555_______34

Solution for the system:
3.000000
1.000000
2.000000

Solution for the system:
3.000000
1.000000
2.000000

2_______1_______3 // method47

// method32_______554_______5

// C++ program to demonstrate working of Gaussian Elimination6_______561_______1 #include<bits/stdc++.h>0

Solution for the system:
3.000000
1.000000
2.000000

1 #include<bits/stdc++.h>25// method77#include<bits/stdc++.h>87

// C++ program to demonstrate working of Gaussian Elimination6_______554_______5

// method64____1_______52

// method64

Solution for the system:
3.000000
1.000000
2.000000

Solution for the system:
3.000000
1.000000
2.000000

// method64

Solution for the system:
3.000000
1.000000
2.000000

1 #include<bits/stdc++.h>97

Solution for the system:
3.000000
1.000000
2.000000

1#include<bits/stdc++.h>99

// method64

Solution for the system:
3.000000
1.000000
2.000000

// method64// function to reduce matrix to r.e.f. Returns a value to1 #include<bits/stdc++.h>0

Solution for the system:
3.000000
1.000000
2.000000

1 using06// method60using08

// method8____555_______4 using11

// method8____554_______5

using14____556_______97

Solution for the system:
3.000000
1.000000
2.000000

1using17

using14____557_______19

// method8____559_______0

// method64

Solution for the system:
3.000000
1.000000
2.000000

// C++ program to demonstrate working of Gaussian Elimination02____1_______76

// C++ program to demonstrate working of Gaussian Elimination02____1_______78

// method64____555_______4 using30// method77// method61

// method8namespace7

Solution for the system:
3.000000
1.000000
2.000000

Solution for the system:
3.000000
1.000000
2.000000

// method64____557_______38

// C++ program to demonstrate working of Gaussian Elimination02____557_______40

// method64____555_______4

Solution for the system:
3.000000
1.000000
2.000000

// method8

Solution for the system:
3.000000
1.000000
2.000000

// method64// function to reduce matrix to r.e.f. Returns a value to1 #include<bits/stdc++.h>0

Solution for the system:
3.000000
1.000000
2.000000

1 using06// method60using08

// method64____554_______5

// method8using56

using57_______557_______58

using57_______557_______60

// method8

Solution for the system:
3.000000
1.000000
2.000000

3 using63

// method8____557_______65

namespace3_______557_______67

// method8// function to reduce matrix to r.e.f. Returns a value to1 #include<bits/stdc++.h>0

Solution for the system:
3.000000
1.000000
2.000000

1 using72// method60#include<bits/stdc++.h>64

using14____557_______76

// method8____557_______78

using57_______557_______80

// method8____557_______82// method77namespace8

// method64____559_______0

// method64____557_______88

// C++ program to demonstrate working of Gaussian Elimination6_______559_______0

// C++ program to demonstrate working of Gaussian Elimination6_______557_______92

// C++ program to demonstrate working of Gaussian Elimination6_______558_______7 using95// method60namespace8

// method32_______559_______0

// method32____1_______5

// method32_______555_______34

Solution for the system:
3.000000
1.000000
2.000000

Solution for the system:
3.000000
1.000000
2.000000

7_______1_______3 // method47

// method32_______554_______5

// C++ program to demonstrate working of Gaussian Elimination6______1_______3 namespace12

// method64namespace14_______558_______15

Solution for the system:
3.000000
1.000000
2.000000

3namespace17// C++ program to demonstrate working of Gaussian Elimination43

// C++ program to demonstrate working of Gaussian Elimination6_______554_______45

#include<bits/stdc++.h>5____554_______47

// C++ program to demonstrate working of Gaussian Elimination6_______561_______1 #include<bits/stdc++.h>0

Solution for the system:
3.000000
1.000000
2.000000

1 namespace27// method60namespace29// method77namespace31

// C++ program to demonstrate working of Gaussian Elimination6_______554_______5

// method64____554_______56

// method64____554_______58

// method64____554_______60

// C++ program to demonstrate working of Gaussian Elimination09____554_______62

// method64// function to reduce matrix to r.e.f. Returns a value to1 #include<bits/stdc++.h>0

Solution for the system:
3.000000
1.000000
2.000000

1 namespace46// method60namespace48

// method64____554_______5

// method8____554_______71

using57_______554_______73

using57_______554_______75

// method8namespace58

// method64____559_______0

// method64____554_______81

// C++ program to demonstrate working of Gaussian Elimination09____554_______83

// method64____558_______66

// C++ program to demonstrate working of Gaussian Elimination6_______559_______0

// C++ program to demonstrate working of Gaussian Elimination6_______556_______68

// C++ program to demonstrate working of Gaussian Elimination6_______555_______65namespace73#include<bits/stdc++.h>2

// C++ program to demonstrate working of Gaussian Elimination6_______561_______1 #include<bits/stdc++.h>0

Solution for the system:
3.000000
1.000000
2.000000

1 #include<bits/stdc++.h>55// method77using08

// C++ program to demonstrate working of Gaussian Elimination6_______554_______5

// method64____558_______85namespace86// method02

// method64____556_______68

// C++ program to demonstrate working of Gaussian Elimination6_______559_______0

// method32_______559_______0

// method32_______555_______04

// method32_______555_______33 // method34

Solution for the system:
3.000000
1.000000
2.000000

6 std;00

// method32_______554_______5

// C++ program to demonstrate working of Gaussian Elimination6_______555_______09

// C++ program to demonstrate working of Gaussian Elimination6_______1_______3 std;07std;08std;09std;10std;11std;12std;09std;08 std;15

std;16_______554_______5std;10std;09std;08std;09std;08std;09std;24 std;15

std;16_______554_______5std;28std;11// method37std;09std;32std;09std;34 std;35

// C++ program to demonstrate working of Gaussian Elimination6_______555_______20

// method32_______559_______0

std;0

std;41

Python3

std;42

std;43

std;44____558_______14 // method37

std;47

std;48 std;49

// C++ program to demonstrate working of Gaussian Elimination6_______559_______51

// C++ program to demonstrate working of Gaussian Elimination6_______559_______53____558_______14 std;55

// C++ program to demonstrate working of Gaussian Elimination6_______559_______57

// C++ program to demonstrate working of Gaussian Elimination6_______555_______4 std;60namespace14 using95// method60std;64

// method8std;66#include<bits/stdc++.h>0// method66// method61

// method8____559_______71

// method8std;73

// method8____559_______75

// method8____555_______4 std;78

using2std;66#include<bits/stdc++.h>0using5// method61

// method8____557_______8std;86

using2std;66#include<bits/stdc++.h>0// method88// method61

// method8namespace7

// C++ program to demonstrate working of Gaussian Elimination6_______559_______95

// C++ program to demonstrate working of Gaussian Elimination6_______559_______97

// C++ program to demonstrate working of Gaussian Elimination6_______559_______99

#define N 3 // Number of unknowns00

std;48 #define N 3 // Number of unknowns02

// C++ program to demonstrate working of Gaussian Elimination6_______561_______1 #define N 3 // Number of unknowns05_______560_______06 #define N 3 // Number of unknowns07#define N 3 // Number of unknowns08#define N 3 // Number of unknowns09 // method60std;64

// method8#define N 3 // Number of unknowns13namespace14 #define N 3 // Number of unknowns15

// method8#define N 3 // Number of unknowns15namespace14 #define N 3 // Number of unknowns19

// method8#define N 3 // Number of unknowns19namespace14 #define N 3 // Number of unknowns13

#define N 3 // Number of unknowns24

std;48 #define N 3 // Number of unknowns26

// C++ program to demonstrate working of Gaussian Elimination6_______561_______1 #define N 3 // Number of unknowns05#define N 3 // Number of unknowns06 #define N 3 // Number of unknowns07#define N 3 // Number of unknowns32

// method64

// method8____560_______35

// method8#define N 3 // Number of unknowns37____558_______14 #define N 3 // Number of unknowns05

// method8____560_______41namespace14 #define N 3 // Number of unknowns43

// method8____560_______45

// method8// function to reduce matrix to r.e.f. Returns a value to1 #define N 3 // Number of unknowns48_______560_______06 #define N 3 // Number of unknowns07#define N 3 // Number of unknowns51#define N 3 // Number of unknowns09 // method60#define N 3 // Number of unknowns54

using2____555_______4 #include<bits/stdc++.h>0

Solution for the system:
3.000000
1.000000
2.000000

69#define N 3 // Number of unknowns59

Solution for the system:
3.000000
1.000000
2.000000

71_______560_______41____558_______14 #define N 3 // Number of unknowns15

Solution for the system:
3.000000
1.000000
2.000000

71_______560_______37____558_______14 #define N 3 // Number of unknowns48

// method8____560_______69

// method8#define N 3 // Number of unknowns71

// method8____560_______73

// method8____555_______4 #define N 3 // Number of unknowns76 #define N 3 // Number of unknowns77

using2____558_______7 #define N 3 // Number of unknowns80#define N 3 // Number of unknowns81

// method8#define N 3 // Number of unknowns83

// method8____555_______4 #define N 3 // Number of unknowns86namespace14 #define N 3 // Number of unknowns88

using2____560_______90

using2____561_______01

using2____561_______03

using2// function to reduce matrix to r.e.f. Returns a value to05namespace14 #define N 3 // Number of unknowns15// function to reduce matrix to r.e.f. Returns a value to08// function to reduce matrix to r.e.f. Returns a value to09

using2____561_______11

using2____561_______13

using2// function to reduce matrix to r.e.f. Returns a value to1 // function to reduce matrix to r.e.f. Returns a value to16#define N 3 // Number of unknowns06 #define N 3 // Number of unknowns07#define N 3 // Number of unknowns51#define N 3 // Number of unknowns09 // method60// function to reduce matrix to r.e.f. Returns a value to22#define N 3 // Number of unknowns09 // method60std;64

Solution for the system:
3.000000
1.000000
2.000000

71_______561_______27using95namespace14 // function to reduce matrix to r.e.f. Returns a value to30// function to reduce matrix to r.e.f. Returns a value to31// function to reduce matrix to r.e.f. Returns a value to05

using2____561_______34

using2____560_______15namespace14 // method77

// method8// function to reduce matrix to r.e.f. Returns a value to40

// C++ program to demonstrate working of Gaussian Elimination6_______561_______42

// C++ program to demonstrate working of Gaussian Elimination6_______558_______7 using95// method60

// function to reduce matrix to r.e.f. Returns a value to47

std;48 // function to reduce matrix to r.e.f. Returns a value to49

// C++ program to demonstrate working of Gaussian Elimination6_______561_______51namespace14 // function to reduce matrix to r.e.f. Returns a value to53// function to reduce matrix to r.e.f. Returns a value to54 // function to reduce matrix to r.e.f. Returns a value to1 // function to reduce matrix to r.e.f. Returns a value to56_______560_______06 #define N 3 // Number of unknowns07// function to reduce matrix to r.e.f. Returns a value to59// function to reduce matrix to r.e.f. Returns a value to60

// C++ program to demonstrate working of Gaussian Elimination6_______561_______62

// C++ program to demonstrate working of Gaussian Elimination6_______561_______64

// C++ program to demonstrate working of Gaussian Elimination6_______561_______1 #define N 3 // Number of unknowns48_______560_______06 #define N 3 // Number of unknowns07#define N 3 // Number of unknowns08using95// method60std;09using95// method60std;09using95_______555_______95__60__6___5

// method8// function to reduce matrix to r.e.f. Returns a value to81

// method8// function to reduce matrix to r.e.f. Returns a value to83namespace14 // function to reduce matrix to r.e.f. Returns a value to85

// method8// function to reduce matrix to r.e.f. Returns a value to87

// method8// function to reduce matrix to r.e.f. Returns a value to89

// method8// function to reduce matrix to r.e.f. Returns a value to1 // function to reduce matrix to r.e.f. Returns a value to16#define N 3 // Number of unknowns06 #define N 3 // Number of unknowns07// function to reduce matrix to r.e.f. Returns a value to95#define N 3 // Number of unknowns09 // method60#define N 3 // Number of unknowns54

using14

using2

Solution for the system:
3.000000
1.000000
2.000000

001

using2

Solution for the system:
3.000000
1.000000
2.000000

003

using2

Solution for the system:
3.000000
1.000000
2.000000

005

using2// function to reduce matrix to r.e.f. Returns a value to83using95namespace14 // function to reduce matrix to r.e.f. Returns a value to27// function to reduce matrix to r.e.f. Returns a value to31

Solution for the system:
3.000000
1.000000
2.000000

012

// method8

Solution for the system:
3.000000
1.000000
2.000000

014

// method8

Solution for the system:
3.000000
1.000000
2.000000

016

// method8// function to reduce matrix to r.e.f. Returns a value to83namespace14

Solution for the system:
3.000000
1.000000
2.000000

020// function to reduce matrix to r.e.f. Returns a value to08

Solution for the system:
3.000000
1.000000
2.000000

022

// C++ program to demonstrate working of Gaussian Elimination6_______559_______66____556_______0

Solution for the system:
3.000000
1.000000
2.000000

026// method61

// C++ program to demonstrate working of Gaussian Elimination6_______561_______1 #define N 3 // Number of unknowns48____560_______06 #define N 3 // Number of unknowns07#define N 3 // Number of unknowns32

// method8std;66#include<bits/stdc++.h>0

Solution for the system:
3.000000
1.000000
2.000000

037

Solution for the system:
3.000000
1.000000
2.000000

038

Solution for the system:
3.000000
1.000000
2.000000

039

Solution for the system:
3.000000
1.000000
2.000000

040

Solution for the system:
3.000000
1.000000
2.000000

041

Solution for the system:
3.000000
1.000000
2.000000

042

Solution for the system:
3.000000
1.000000
2.000000

043namespace14

Solution for the system:
3.000000
1.000000
2.000000

045std;08std;09std;10std;09using95std;12std;09std;08

Solution for the system:
3.000000
1.000000
2.000000

054std;10std;09std;08std;09std;08std;09std;24

Solution for the system:
3.000000
1.000000
2.000000

054std;28std;09using95// method37std;09std;32std;09std;34

Solution for the system:
3.000000
1.000000
2.000000

071

Solution for the system:
3.000000
1.000000
2.000000

072

Solution for the system:
3.000000
1.000000
2.000000

073

C#

Solution for the system:
3.000000
1.000000
2.000000

074

Solution for the system:
3.000000
1.000000
2.000000

075

using

Solution for the system:
3.000000
1.000000
2.000000

077

// method29

Solution for the system:
3.000000
1.000000
2.000000

079

// C++ program to demonstrate working of Gaussian Elimination6

// method39

// method33 // method34

Solution for the system:
3.000000
1.000000
2.000000

Solution for the system:
3.000000
1.000000
2.000000

085

Solution for the system:
3.000000
1.000000
2.000000

086

// method34

Solution for the system:
3.000000
1.000000
2.000000

6 // C++ program to demonstrate working of Gaussian Elimination2

Solution for the system:
3.000000
1.000000
2.000000

Solution for the system:
3.000000
1.000000
2.000000

091

// C++ program to demonstrate working of Gaussian Elimination5

// C++ program to demonstrate working of Gaussian Elimination6_______554_______7

// C++ program to demonstrate working of Gaussian Elimination6______1_______1 // method0

// C++ program to demonstrate working of Gaussian Elimination6

// C++ program to demonstrate working of Gaussian Elimination6_______555_______2

// C++ program to demonstrate working of Gaussian Elimination6_______555_______4 // method5

// C++ program to demonstrate working of Gaussian Elimination6_______554_______5

// method8

Solution for the system:
3.000000
1.000000
2.000000

107_______555_______66#include<bits/stdc++.h>2

// method8

// method8#include<bits/stdc++.h>4

#include<bits/stdc++.h>5____556_______6

#include<bits/stdc++.h>5____556_______8

// method8// method4

Solution for the system:
3.000000
1.000000
2.000000

119

using2

Solution for the system:
3.000000
1.000000
2.000000

121_______557_______5#include<bits/stdc++.h>2

// method8using8

using2

Solution for the system:
3.000000
1.000000
2.000000

121

Solution for the system:
3.000000
1.000000
2.000000

128 #define N 3 // Number of unknowns09

// method13_______1_______131#include<bits/stdc++.h>2

// method8

// method8____558_______7namespace8

// C++ program to demonstrate working of Gaussian Elimination6_______559_______0

// C++ program to demonstrate working of Gaussian Elimination6

// C++ program to demonstrate working of Gaussian Elimination6_______559_______2

// C++ program to demonstrate working of Gaussian Elimination6_______559_______4

// C++ program to demonstrate working of Gaussian Elimination6_______559_______6

std;0

Solution for the system:
3.000000
1.000000
2.000000

147

#include<bits/stdc++.h>06

// method34

Solution for the system:
3.000000
1.000000
2.000000

6 #define N 3 // Number of unknowns0

Solution for the system:
3.000000
1.000000
2.000000

Solution for the system:
3.000000
1.000000
2.000000

153

Solution for the system:
3.000000
1.000000
2.000000

1 #define N 3 // Number of unknowns4

Solution for the system:
3.000000
1.000000
2.000000

1 #define N 3 // Number of unknowns6

// C++ program to demonstrate working of Gaussian Elimination5

// C++ program to demonstrate working of Gaussian Elimination6

// C++ program to demonstrate working of Gaussian Elimination6_______556_______20

// C++ program to demonstrate working of Gaussian Elimination6

// C++ program to demonstrate working of Gaussian Elimination6_______561_______1#include<bits/stdc++.h>0

Solution for the system:
3.000000
1.000000
2.000000

Solution for the system:
3.000000
1.000000
2.000000

167

// C++ program to demonstrate working of Gaussian Elimination6_______554_______5

// method8

Solution for the system:
3.000000
1.000000
2.000000

Solution for the system:
3.000000
1.000000
2.000000

172

// method8

Solution for the system:
3.000000
1.000000
2.000000

174

// method8

Solution for the system:
3.000000
1.000000
2.000000

176

// C++ program to demonstrate working of Gaussian Elimination6_______559_______0

std;0

// C++ program to demonstrate working of Gaussian Elimination6

Solution for the system:
3.000000
1.000000
2.000000

181

// method34

Solution for the system:
3.000000
1.000000
2.000000

Solution for the system:
3.000000
1.000000
2.000000

Solution for the system:
3.000000
1.000000
2.000000

Solution for the system:
3.000000
1.000000
2.000000

091

// C++ program to demonstrate working of Gaussian Elimination5

// C++ program to demonstrate working of Gaussian Elimination6_______561_______1#include<bits/stdc++.h>0

Solution for the system:
3.000000
1.000000
2.000000

Solution for the system:
3.000000
1.000000
2.000000

192

// method8// function to reduce matrix to r.e.f. Returns a value to1#include<bits/stdc++.h>0

Solution for the system:
3.000000
1.000000
2.000000

Solution for the system:
3.000000
1.000000
2.000000

197

using2

Solution for the system:
3.000000
1.000000
2.000000

199

using2

// C++ program to demonstrate working of Gaussian Elimination6______1_______202

std;0

Solution for the system:
3.000000
1.000000
2.000000

204

// method34

Solution for the system:
3.000000
1.000000
2.000000

Solution for the system:
3.000000
1.000000
2.000000

Solution for the system:
3.000000
1.000000
2.000000

Solution for the system:
3.000000
1.000000
2.000000

091

// C++ program to demonstrate working of Gaussian Elimination5

// C++ program to demonstrate working of Gaussian Elimination6_______561_______1#include<bits/stdc++.h>0

Solution for the system:
3.000000
1.000000
2.000000

Solution for the system:
3.000000
1.000000
2.000000

215

// C++ program to demonstrate working of Gaussian Elimination6_______554_______5

// method8

Solution for the system:
3.000000
1.000000
2.000000

// method8

Solution for the system:
3.000000
1.000000
2.000000

Solution for the system:
3.000000
1.000000
2.000000

// method8

Solution for the system:
3.000000
1.000000
2.000000

1 #include<bits/stdc++.h>97

Solution for the system:
3.000000
1.000000
2.000000

Solution for the system:
3.000000
1.000000
2.000000

228

// method8

Solution for the system:
3.000000
1.000000
2.000000

// method8// function to reduce matrix to r.e.f. Returns a value to1#include<bits/stdc++.h>0

Solution for the system:
3.000000
1.000000
2.000000

Solution for the system:
3.000000
1.000000
2.000000

236

// method8____554_______5

using2____555_______4

Solution for the system:
3.000000
1.000000
2.000000

241

using2____554_______5

Solution for the system:
3.000000
1.000000
2.000000

71_______556_______97

Solution for the system:
3.000000
1.000000
2.000000

Solution for the system:
3.000000
1.000000
2.000000

247

Solution for the system:
3.000000
1.000000
2.000000

71____557_______19

using2____559_______0

// method8

using2

Solution for the system:
3.000000
1.000000
2.000000

254

using2

Solution for the system:
3.000000
1.000000
2.000000

256

using2

Solution for the system:
3.000000
1.000000
2.000000

258

using2____555_______4

Solution for the system:
3.000000
1.000000
2.000000

261

Solution for the system:
3.000000
1.000000
2.000000

71_______558_______7

Solution for the system:
3.000000
1.000000
2.000000

Solution for the system:
3.000000
1.000000
2.000000

using2

Solution for the system:
3.000000
1.000000
2.000000

268

// C++ program to demonstrate working of Gaussian Elimination09____1_______270

using2____557_______40

using2____555_______4

Solution for the system:
3.000000
1.000000
2.000000

Solution for the system:
3.000000
1.000000
2.000000

71______1_______92

using2

using2____561_______1____556_______0

Solution for the system:
3.000000
1.000000
2.000000

Solution for the system:
3.000000
1.000000
2.000000

283

using2____554_______5

using2

Solution for the system:
3.000000
1.000000
2.000000

71____557_______56

Solution for the system:
3.000000
1.000000
2.000000

71______1_______290

Solution for the system:
3.000000
1.000000
2.000000

71____1_______292

Solution for the system:
3.000000
1.000000
2.000000

71______1_______3

Solution for the system:
3.000000
1.000000
2.000000

295

Solution for the system:
3.000000
1.000000
2.000000

Solution for the system:
3.000000
1.000000
2.000000

71____557_______65

namespace3_______557_______67

Solution for the system:
3.000000
1.000000
2.000000

71_______561_______1#include<bits/stdc++.h>0

Solution for the system:
3.000000
1.000000
2.000000

Solution for the system:
3.000000
1.000000
2.000000

305

Solution for the system:
3.000000
1.000000
2.000000

306____1_______307

Solution for the system:
3.000000
1.000000
2.000000

Solution for the system:
3.000000
1.000000
2.000000

71____557_______78

Solution for the system:
3.000000
1.000000
2.000000

71______1_______312

Solution for the system:
3.000000
1.000000
2.000000

71______1_______314

using2____559_______0

// method8____559_______0

// method8using88

// C++ program to demonstrate working of Gaussian Elimination6_______559_______0

// C++ program to demonstrate working of Gaussian Elimination6

// C++ program to demonstrate working of Gaussian Elimination6_______557_______92

// C++ program to demonstrate working of Gaussian Elimination6_______558_______7 // C++ program to demonstrate working of Gaussian Elimination32

std;0

Solution for the system:
3.000000
1.000000
2.000000

330

// method34

Solution for the system:
3.000000
1.000000
2.000000

Solution for the system:
3.000000
1.000000
2.000000

Solution for the system:
3.000000
1.000000
2.000000

Solution for the system:
3.000000
1.000000
2.000000

091

// C++ program to demonstrate working of Gaussian Elimination5

// C++ program to demonstrate working of Gaussian Elimination6

// C++ program to demonstrate working of Gaussian Elimination6_______554_______43

// C++ program to demonstrate working of Gaussian Elimination6_______1_______3

Solution for the system:
3.000000
1.000000
2.000000

342namespace15

Solution for the system:
3.000000
1.000000
2.000000

3namespace17

// C++ program to demonstrate working of Gaussian Elimination6

// C++ program to demonstrate working of Gaussian Elimination6_______554_______45

std;3____554_______47

// C++ program to demonstrate working of Gaussian Elimination6_______561_______1#include<bits/stdc++.h>0

Solution for the system:
3.000000
1.000000
2.000000

Solution for the system:
3.000000
1.000000
2.000000

355

// C++ program to demonstrate working of Gaussian Elimination6_______554_______5

// C++ program to demonstrate working of Gaussian Elimination6

// method8____554_______56

// method8

Solution for the system:
3.000000
1.000000
2.000000

362

// method8

// method8____554_______60

// method8____554_______62

// method8// function to reduce matrix to r.e.f. Returns a value to1#include<bits/stdc++.h>0

Solution for the system:
3.000000
1.000000
2.000000

Solution for the system:
3.000000
1.000000
2.000000

372

// method8____554_______5

// method8

using2____554_______71

// C++ program to demonstrate working of Gaussian Elimination02____554_______73

// C++ program to demonstrate working of Gaussian Elimination02____554_______75

using2____1_______383

// method8____559_______0

// method8

// method8____554_______81

// method8// C++ program to demonstrate working of Gaussian Elimination83

// method8

Solution for the system:
3.000000
1.000000
2.000000

392

// C++ program to demonstrate working of Gaussian Elimination6_______559_______0

// C++ program to demonstrate working of Gaussian Elimination6

// C++ program to demonstrate working of Gaussian Elimination6______1_______202

// C++ program to demonstrate working of Gaussian Elimination6_______1_______107____558_______73#include<bits/stdc++.h>2

// C++ program to demonstrate working of Gaussian Elimination6_______561_______1#include<bits/stdc++.h>0

Solution for the system:
3.000000
1.000000
2.000000

Solution for the system:
3.000000
1.000000
2.000000

406

// C++ program to demonstrate working of Gaussian Elimination6_______554_______5

// method8

Solution for the system:
3.000000
1.000000
2.000000

121

Solution for the system:
3.000000
1.000000
2.000000

411// method02

// method8

Solution for the system:
3.000000
1.000000
2.000000

202

// C++ program to demonstrate working of Gaussian Elimination6_______559_______0

std;0

Solution for the system:
3.000000
1.000000
2.000000

418

// method33 // method34

Solution for the system:
3.000000
1.000000
2.000000

Solution for the system:
3.000000
1.000000
2.000000

422

// C++ program to demonstrate working of Gaussian Elimination5

// C++ program to demonstrate working of Gaussian Elimination6

// C++ program to demonstrate working of Gaussian Elimination6_______555_______09

// C++ program to demonstrate working of Gaussian Elimination6______1_______3

Solution for the system:
3.000000
1.000000
2.000000

429

std;16______1_______431

std;16______1_______433

// C++ program to demonstrate working of Gaussian Elimination6

// C++ program to demonstrate working of Gaussian Elimination6_______555_______20

std;0

Solution for the system:
3.000000
1.000000
2.000000

439

PHP

Solution for the system:
3.000000
1.000000
2.000000

440

Solution for the system:
3.000000
1.000000
2.000000

441

Solution for the system:
3.000000
1.000000
2.000000

075

Solution for the system:
3.000000
1.000000
2.000000

443

Solution for the system:
3.000000
1.000000
2.000000

444// method39

// C++ program to demonstrate working of Gaussian Elimination0

Solution for the system:
3.000000
1.000000
2.000000

447 // C++ program to demonstrate working of Gaussian Elimination2

Solution for the system:
3.000000
1.000000
2.000000

449// method61

// C++ program to demonstrate working of Gaussian Elimination5

// C++ program to demonstrate working of Gaussian Elimination6_______1_______453

Solution for the system:
3.000000
1.000000
2.000000

443namespace8

// C++ program to demonstrate working of Gaussian Elimination6

// C++ program to demonstrate working of Gaussian Elimination6_______554_______7

// C++ program to demonstrate working of Gaussian Elimination6_______1_______460

Solution for the system:
3.000000
1.000000
2.000000

461

Solution for the system:
3.000000
1.000000
2.000000

449#include<bits/stdc++.h>2

// C++ program to demonstrate working of Gaussian Elimination6_______555_______2

// C++ program to demonstrate working of Gaussian Elimination6_______555_______4 #include<bits/stdc++.h>0

Solution for the system:
3.000000
1.000000
2.000000

460

Solution for the system:
3.000000
1.000000
2.000000

470

// C++ program to demonstrate working of Gaussian Elimination6_______554_______5

// method8std;66#include<bits/stdc++.h>0#include<bits/stdc++.h>1#include<bits/stdc++.h>2

// method8#include<bits/stdc++.h>4

// method8

Solution for the system:
3.000000
1.000000
2.000000

481

// method8#include<bits/stdc++.h>8

// method8// method4 #include<bits/stdc++.h>0

Solution for the system:
3.000000
1.000000
2.000000

449// function to reduce matrix to r.e.f. Returns a value to53

Solution for the system:
3.000000
1.000000
2.000000

460

Solution for the system:
3.000000
1.000000
2.000000

490_______1_______443

Solution for the system:
3.000000
1.000000
2.000000

492

using2std;66#include<bits/stdc++.h>0using5#include<bits/stdc++.h>2

// method8using8

using2std;66#include<bits/stdc++.h>0// method88#include<bits/stdc++.h>2

// method8____558_______7namespace8

// C++ program to demonstrate working of Gaussian Elimination6_______559_______0

// C++ program to demonstrate working of Gaussian Elimination6_______559_______2

// C++ program to demonstrate working of Gaussian Elimination6_______559_______4

// C++ program to demonstrate working of Gaussian Elimination6_______1_______7

Solution for the system:
3.000000
1.000000
2.000000

449#include<bits/stdc++.h>2

std;0

Solution for the system:
3.000000
1.000000
2.000000

519

Solution for the system:
3.000000
1.000000
2.000000

520

Solution for the system:
3.000000
1.000000
2.000000

447

Solution for the system:
3.000000
1.000000
2.000000

522

Solution for the system:
3.000000
1.000000
2.000000

449std;09

Solution for the system:
3.000000
1.000000
2.000000

525std;09

Solution for the system:
3.000000
1.000000
2.000000

527// method61

// C++ program to demonstrate working of Gaussian Elimination5

// C++ program to demonstrate working of Gaussian Elimination6_______1_______453

Solution for the system:
3.000000
1.000000
2.000000

443namespace8

// C++ program to demonstrate working of Gaussian Elimination6_______560_______9

// C++ program to demonstrate working of Gaussian Elimination6_______561_______1 #include<bits/stdc++.h>0

Solution for the system:
3.000000
1.000000
2.000000

539

Solution for the system:
3.000000
1.000000
2.000000

540

Solution for the system:
3.000000
1.000000
2.000000

539

Solution for the system:
3.000000
1.000000
2.000000

542

Solution for the system:
3.000000
1.000000
2.000000

443namespace8

Solution for the system:
3.000000
1.000000
2.000000

539

Solution for the system:
3.000000
1.000000
2.000000

546

// C++ program to demonstrate working of Gaussian Elimination6_______554_______5

// method8

Solution for the system:
3.000000
1.000000
2.000000

550 namespace14

Solution for the system:
3.000000
1.000000
2.000000

449// function to reduce matrix to r.e.f. Returns a value to53

Solution for the system:
3.000000
1.000000
2.000000

525

Solution for the system:
3.000000
1.000000
2.000000

490

Solution for the system:
3.000000
1.000000
2.000000

539

Solution for the system:
3.000000
1.000000
2.000000

557

// method8

Solution for the system:
3.000000
1.000000
2.000000

449// function to reduce matrix to r.e.f. Returns a value to53

Solution for the system:
3.000000
1.000000
2.000000

525

Solution for the system:
3.000000
1.000000
2.000000

490

Solution for the system:
3.000000
1.000000
2.000000

539

Solution for the system:
3.000000
1.000000
2.000000

564

Solution for the system:
3.000000
1.000000
2.000000

449// function to reduce matrix to r.e.f. Returns a value to53

Solution for the system:
3.000000
1.000000
2.000000

527

Solution for the system:
3.000000
1.000000
2.000000

490

Solution for the system:
3.000000
1.000000
2.000000

539

Solution for the system:
3.000000
1.000000
2.000000

557

// method8

Solution for the system:
3.000000
1.000000
2.000000

449// function to reduce matrix to r.e.f. Returns a value to53

Solution for the system:
3.000000
1.000000
2.000000

527

Solution for the system:
3.000000
1.000000
2.000000

490

Solution for the system:
3.000000
1.000000
2.000000

539

Solution for the system:
3.000000
1.000000
2.000000

564

Solution for the system:
3.000000
1.000000
2.000000

550namespace8

// C++ program to demonstrate working of Gaussian Elimination6_______559_______0

std;0

Solution for the system:
3.000000
1.000000
2.000000

Solution for the system:
3.000000
1.000000
2.000000

447

Solution for the system:
3.000000
1.000000
2.000000

585

Solution for the system:
3.000000
1.000000
2.000000

449// method61

// C++ program to demonstrate working of Gaussian Elimination5

// C++ program to demonstrate working of Gaussian Elimination6_______1_______453

Solution for the system:
3.000000
1.000000
2.000000

443namespace8

// C++ program to demonstrate working of Gaussian Elimination6_______561_______1 #include<bits/stdc++.h>0

Solution for the system:
3.000000
1.000000
2.000000

525_______1_______597

Solution for the system:
3.000000
1.000000
2.000000

525

Solution for the system:
3.000000
1.000000
2.000000

599

Solution for the system:
3.000000
1.000000
2.000000

443namespace8

Solution for the system:
3.000000
1.000000
2.000000

525

Solution for the system:
3.000000
1.000000
2.000000

603std;66#include<bits/stdc++.h>0

Solution for the system:
3.000000
1.000000
2.000000

20_______1_______21

// method8// function to reduce matrix to r.e.f. Returns a value to1 #include<bits/stdc++.h>0

Solution for the system:
3.000000
1.000000
2.000000

527

Solution for the system:
3.000000
1.000000
2.000000

597

Solution for the system:
3.000000
1.000000
2.000000

527

Solution for the system:
3.000000
1.000000
2.000000

542_______1_______443namespace8

Solution for the system:
3.000000
1.000000
2.000000

527

Solution for the system:
3.000000
1.000000
2.000000

546

using2std;66#include<bits/stdc++.h>0_______1_______449// function to reduce matrix to r.e.f. Returns a value to53

Solution for the system:
3.000000
1.000000
2.000000

525

Solution for the system:
3.000000
1.000000
2.000000

490

Solution for the system:
3.000000
1.000000
2.000000

527

Solution for the system:
3.000000
1.000000
2.000000

627

// C++ program to demonstrate working of Gaussian Elimination6_______559_______66____556_______0

Solution for the system:
3.000000
1.000000
2.000000

20#include<bits/stdc++.h>2

std;0

Solution for the system:
3.000000
1.000000
2.000000

Solution for the system:
3.000000
1.000000
2.000000

447

Solution for the system:
3.000000
1.000000
2.000000

636

Solution for the system:
3.000000
1.000000
2.000000

449// method61

// C++ program to demonstrate working of Gaussian Elimination5

// C++ program to demonstrate working of Gaussian Elimination6_______1_______453

Solution for the system:
3.000000
1.000000
2.000000

443namespace8

// C++ program to demonstrate working of Gaussian Elimination6_______561_______1 #include<bits/stdc++.h>0

Solution for the system:
3.000000
1.000000
2.000000

539

Solution for the system:
3.000000
1.000000
2.000000

597

Solution for the system:
3.000000
1.000000
2.000000

539

Solution for the system:
3.000000
1.000000
2.000000

599

Solution for the system:
3.000000
1.000000
2.000000

443namespace8

Solution for the system:
3.000000
1.000000
2.000000

539

Solution for the system:
3.000000
1.000000
2.000000

546

// C++ program to demonstrate working of Gaussian Elimination6_______554_______5

// method8

Solution for the system:
3.000000
1.000000
2.000000

// method8

Solution for the system:
3.000000
1.000000
2.000000

660 namespace14

Solution for the system:
3.000000
1.000000
2.000000

539namespace8

// method8

Solution for the system:
3.000000
1.000000
2.000000

665 namespace14

Solution for the system:
3.000000
1.000000
2.000000

449// function to reduce matrix to r.e.f. Returns a value to53

Solution for the system:
3.000000
1.000000
2.000000

660

Solution for the system:
3.000000
1.000000
2.000000

490

Solution for the system:
3.000000
1.000000
2.000000

539

Solution for the system:
3.000000
1.000000
2.000000

557

// method8

Solution for the system:
3.000000
1.000000
2.000000

// method8// function to reduce matrix to r.e.f. Returns a value to1 #include<bits/stdc++.h>0

Solution for the system:
3.000000
1.000000
2.000000

525 namespace14

Solution for the system:
3.000000
1.000000
2.000000

539

Solution for the system:
3.000000
1.000000
2.000000

681

Solution for the system:
3.000000
1.000000
2.000000

525

Solution for the system:
3.000000
1.000000
2.000000

599

Solution for the system:
3.000000
1.000000
2.000000

443namespace8

Solution for the system:
3.000000
1.000000
2.000000

525

Solution for the system:
3.000000
1.000000
2.000000

546

using2// method4 #include<bits/stdc++.h>0

Solution for the system:
3.000000
1.000000
2.000000

69#include<bits/stdc++.h>0

Solution for the system:
3.000000
1.000000
2.000000

449// function to reduce matrix to r.e.f. Returns a value to53_______1_______525

Solution for the system:
3.000000
1.000000
2.000000

490

Solution for the system:
3.000000
1.000000
2.000000

539

Solution for the system:
3.000000
1.000000
2.000000

698

Solution for the system:
3.000000
1.000000
2.000000

665// method61

Solution for the system:
3.000000
1.000000
2.000000

71____554_______5

Solution for the system:
3.000000
1.000000
2.000000

306_______1_______665 namespace14

Solution for the system:
3.000000
1.000000
2.000000

449// function to reduce matrix to r.e.f. Returns a value to53

Solution for the system:
3.000000
1.000000
2.000000

525

Solution for the system:
3.000000
1.000000
2.000000

490

Solution for the system:
3.000000
1.000000
2.000000

539

Solution for the system:
3.000000
1.000000
2.000000

557

Solution for the system:
3.000000
1.000000
2.000000

306_______1_______660 namespace14

Solution for the system:
3.000000
1.000000
2.000000

525namespace8

Solution for the system:
3.000000
1.000000
2.000000

71____559_______0

// method8

Solution for the system:
3.000000
1.000000
2.000000

720

// method8

Solution for the system:
3.000000
1.000000
2.000000

// method8

Solution for the system:
3.000000
1.000000
2.000000

// method8// method4

Solution for the system:
3.000000
1.000000
2.000000

727

Solution for the system:
3.000000
1.000000
2.000000

449// function to reduce matrix to r.e.f. Returns a value to53

Solution for the system:
3.000000
1.000000
2.000000

539

Solution for the system:
3.000000
1.000000
2.000000

490_______1_______660

Solution for the system:
3.000000
1.000000
2.000000

492

using2____558_______7

Solution for the system:
3.000000
1.000000
2.000000

539namespace8

Solution for the system:
3.000000
1.000000
2.000000

// method8

Solution for the system:
3.000000
1.000000
2.000000

// method8// method4 #include<bits/stdc++.h>0

Solution for the system:
3.000000
1.000000
2.000000

660

Solution for the system:
3.000000
1.000000
2.000000

745

Solution for the system:
3.000000
1.000000
2.000000

539// method61

using2#define N 3 // Number of unknowns0

Solution for the system:
3.000000
1.000000
2.000000

449_______559_______09

Solution for the system:
3.000000
1.000000
2.000000

539std;09

Solution for the system:
3.000000
1.000000
2.000000

660#include<bits/stdc++.h>2

// method8// function to reduce matrix to r.e.f. Returns a value to1 #include<bits/stdc++.h>0

Solution for the system:
3.000000
1.000000
2.000000

525 namespace14

Solution for the system:
3.000000
1.000000
2.000000

539

Solution for the system:
3.000000
1.000000
2.000000

762

Solution for the system:
3.000000
1.000000
2.000000

525

Solution for the system:
3.000000
1.000000
2.000000

599

Solution for the system:
3.000000
1.000000
2.000000

443namespace8

Solution for the system:
3.000000
1.000000
2.000000

525

Solution for the system:
3.000000
1.000000
2.000000

546

// method8____554_______5

using2____554_______01

using2____554_______03

using2

Solution for the system:
3.000000
1.000000
2.000000

776 namespace14_______1_______449// function to reduce matrix to r.e.f. Returns a value to53

Solution for the system:
3.000000
1.000000
2.000000

525

Solution for the system:
3.000000
1.000000
2.000000

490

Solution for the system:
3.000000
1.000000
2.000000

539

Solution for the system:
3.000000
1.000000
2.000000

783

Solution for the system:
3.000000
1.000000
2.000000

449// function to reduce matrix to r.e.f. Returns a value to53

Solution for the system:
3.000000
1.000000
2.000000

539

Solution for the system:
3.000000
1.000000
2.000000

490

Solution for the system:
3.000000
1.000000
2.000000

539_______1_______557

using2____554_______08

using2____554_______10

using2// function to reduce matrix to r.e.f. Returns a value to1 #include<bits/stdc++.h>0

Solution for the system:
3.000000
1.000000
2.000000

527 namespace14

Solution for the system:
3.000000
1.000000
2.000000

539

Solution for the system:
3.000000
1.000000
2.000000

762

Solution for the system:
3.000000
1.000000
2.000000

527

Solution for the system:
3.000000
1.000000
2.000000

542

Solution for the system:
3.000000
1.000000
2.000000

443namespace8

Solution for the system:
3.000000
1.000000
2.000000

527

Solution for the system:
3.000000
1.000000
2.000000

546

Solution for the system:
3.000000
1.000000
2.000000

71_______1_______449// function to reduce matrix to r.e.f. Returns a value to53

Solution for the system:
3.000000
1.000000
2.000000

525

Solution for the system:
3.000000
1.000000
2.000000

490

Solution for the system:
3.000000
1.000000
2.000000

527

Solution for the system:
3.000000
1.000000
2.000000

813

Solution for the system:
3.000000
1.000000
2.000000

449// function to reduce matrix to r.e.f. Returns a value to53

Solution for the system:
3.000000
1.000000
2.000000

539

Solution for the system:
3.000000
1.000000
2.000000

490

Solution for the system:
3.000000
1.000000
2.000000

527

Solution for the system:
3.000000
1.000000
2.000000

819

Solution for the system:
3.000000
1.000000
2.000000

776namespace8

using2____554_______19

using2

Solution for the system:
3.000000
1.000000
2.000000

449// function to reduce matrix to r.e.f. Returns a value to53

Solution for the system:
3.000000
1.000000
2.000000

525

Solution for the system:
3.000000
1.000000
2.000000

490

Solution for the system:
3.000000
1.000000
2.000000

539

Solution for the system:
3.000000
1.000000
2.000000

830

// method8____559_______0

// method8

Solution for the system:
3.000000
1.000000
2.000000

834

// C++ program to demonstrate working of Gaussian Elimination6_______559_______0

// C++ program to demonstrate working of Gaussian Elimination6______1_______838

// C++ program to demonstrate working of Gaussian Elimination6_______558_______7 // C++ program to demonstrate working of Gaussian Elimination32

std;0

Solution for the system:
3.000000
1.000000
2.000000

Solution for the system:
3.000000
1.000000
2.000000

447

Solution for the system:
3.000000
1.000000
2.000000

845

Solution for the system:
3.000000
1.000000
2.000000

449// method61

// C++ program to demonstrate working of Gaussian Elimination5

// C++ program to demonstrate working of Gaussian Elimination6_______1_______453

Solution for the system:
3.000000
1.000000
2.000000

443namespace8

// C++ program to demonstrate working of Gaussian Elimination6_______1_______854 namespace14

Solution for the system:
3.000000
1.000000
2.000000

856

Solution for the system:
3.000000
1.000000
2.000000

857

Solution for the system:
3.000000
1.000000
2.000000

443

Solution for the system:
3.000000
1.000000
2.000000

859// C++ program to demonstrate working of Gaussian Elimination43

// C++ program to demonstrate working of Gaussian Elimination6_______554_______45

// C++ program to demonstrate working of Gaussian Elimination6_______554_______47

// C++ program to demonstrate working of Gaussian Elimination6_______561_______1 #include<bits/stdc++.h>0

Solution for the system:
3.000000
1.000000
2.000000

525 namespace14

Solution for the system:
3.000000
1.000000
2.000000

443

Solution for the system:
3.000000
1.000000
2.000000

871

Solution for the system:
3.000000
1.000000
2.000000

525

Solution for the system:
3.000000
1.000000
2.000000

873

Solution for the system:
3.000000
1.000000
2.000000

525

Solution for the system:
3.000000
1.000000
2.000000

875

// C++ program to demonstrate working of Gaussian Elimination6_______554_______5

// method8____554_______56

// method8

Solution for the system:
3.000000
1.000000
2.000000

854// function to reduce matrix to r.e.f. Returns a value to53_______1_______525

Solution for the system:
3.000000
1.000000
2.000000

564

Solution for the system:
3.000000
1.000000
2.000000

449// function to reduce matrix to r.e.f. Returns a value to53

Solution for the system:
3.000000
1.000000
2.000000

525

Solution for the system:
3.000000
1.000000
2.000000

490

Solution for the system:
3.000000
1.000000
2.000000

443

Solution for the system:
3.000000
1.000000
2.000000

557

// method8____554_______60

// method8____554_______62

// method8// function to reduce matrix to r.e.f. Returns a value to1 #include<bits/stdc++.h>0

Solution for the system:
3.000000
1.000000
2.000000

527 namespace14

Solution for the system:
3.000000
1.000000
2.000000

525

Solution for the system:
3.000000
1.000000
2.000000

762

Solution for the system:
3.000000
1.000000
2.000000

527

Solution for the system:
3.000000
1.000000
2.000000

599

Solution for the system:
3.000000
1.000000
2.000000

443namespace8

Solution for the system:
3.000000
1.000000
2.000000

527

Solution for the system:
3.000000
1.000000
2.000000

546

// method8____554_______5

using2____554_______71

using2____554_______73

using2____554_______75

using2

Solution for the system:
3.000000
1.000000
2.000000

854// function to reduce matrix to r.e.f. Returns a value to53

Solution for the system:
3.000000
1.000000
2.000000

525

Solution for the system:
3.000000
1.000000
2.000000

813

Solution for the system:
3.000000
1.000000
2.000000

449// function to reduce matrix to r.e.f. Returns a value to53

Solution for the system:
3.000000
1.000000
2.000000

525

Solution for the system:
3.000000
1.000000
2.000000

490

Solution for the system:
3.000000
1.000000
2.000000

527

Solution for the system:
3.000000
1.000000
2.000000

819

Solution for the system:
3.000000
1.000000
2.000000

854// function to reduce matrix to r.e.f. Returns a value to53

Solution for the system:
3.000000
1.000000
2.000000

527_______1_______557

// method8____559_______0

// method8____554_______81

// method8// C++ program to demonstrate working of Gaussian Elimination83

// method8

Solution for the system:
3.000000
1.000000
2.000000

854// function to reduce matrix to r.e.f. Returns a value to53

Solution for the system:
3.000000
1.000000
2.000000

525

Solution for the system:
3.000000
1.000000
2.000000

564

Solution for the system:
3.000000
1.000000
2.000000

854// function to reduce matrix to r.e.f. Returns a value to53

Solution for the system:
3.000000
1.000000
2.000000

525

Solution for the system:
3.000000
1.000000
2.000000

945

Solution for the system:
3.000000
1.000000
2.000000

449// function to reduce matrix to r.e.f. Returns a value to53

Solution for the system:
3.000000
1.000000
2.000000

525

Solution for the system:
3.000000
1.000000
2.000000

490

Solution for the system:
3.000000
1.000000
2.000000

525_______1_______557

// C++ program to demonstrate working of Gaussian Elimination6_______559_______0

// C++ program to demonstrate working of Gaussian Elimination6_______559_______66____556_______0// C++ program to demonstrate working of Gaussian Elimination91#include<bits/stdc++.h>2

// C++ program to demonstrate working of Gaussian Elimination6_______561_______1 #include<bits/stdc++.h>0

Solution for the system:
3.000000
1.000000
2.000000

525

Solution for the system:
3.000000
1.000000
2.000000

540

Solution for the system:
3.000000
1.000000
2.000000

525

Solution for the system:
3.000000
1.000000
2.000000

599

Solution for the system:
3.000000
1.000000
2.000000

443namespace8

Solution for the system:
3.000000
1.000000
2.000000

525

Solution for the system:
3.000000
1.000000
2.000000

546

// method8std;66

Solution for the system:
3.000000
1.000000
2.000000

972

Solution for the system:
3.000000
1.000000
2.000000

973#include<bits/stdc++.h>0

Solution for the system:
3.000000
1.000000
2.000000

854// function to reduce matrix to r.e.f. Returns a value to53

Solution for the system:
3.000000
1.000000
2.000000

525

Solution for the system:
3.000000
1.000000
2.000000

978

Solution for the system:
3.000000
1.000000
2.000000

20#include<bits/stdc++.h>2

Ví dụ loại bỏ Gaussian là gì?

Phương pháp này, được đặc trưng bởi việc loại bỏ từng bước các biến, được gọi là loại bỏ Gaussian. ví dụ 1. Giải quyết hệ thống này. Nhân phương trình thứ nhất với −3 và cộng kết quả vào phương trình thứ hai sẽ loại bỏ biến x . Phương trình cuối cùng này, −5 y = −5, ngay lập tức hàm ý y = 1.

Loại bỏ Gaussian là ref hay rref?

Khử Gauss-Jordan là một quy trình cơ học để biến đổi một hệ phương trình tuyến tính đã cho thành Rx=d với R trong RREF chỉ sử dụng cơ sở . Nói một cách thông thường, quá trình chuyển đổi ma trận thành RREF được gọi là giảm hàng.

Thuật toán loại bỏ Gaussian là gì?

Thuật toán. Loại bỏ Gaussian nhằm mục đích biến đổi một hệ phương trình tuyến tính thành ma trận tam giác trên để giải các ẩn số và rút ra nghiệm . Một cột trục được sử dụng để thu gọn các hàng trước nó; .