programming python

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)

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 0

Solution for the system: 3.000000 1.000000 2.000000 1 Solution for the system: 3.000000 1.000000 2.000000 2Solution for the system: 3.000000 1.000000 2.000000 3 Solution for the system: 3.000000 1.000000 2.000000 4

Solution for the system: 3.000000 1.000000 2.000000 5

Solution for the system: 3.000000 1.000000 2.000000 6 Solution for the system: 3.000000 1.000000 2.000000 7_______1_______3 Solution for the system: 3.000000 1.000000 2.000000 4

// 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 Elimination2Solution 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 unknowns0Solution for the system: 3.000000 1.000000 2.000000 3 #define N 3 // Number of unknowns2Solution for the system: 3.000000 1.000000 2.000000 1 #define N 3 // Number of unknowns4Solution 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>0Solution 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

// method8Solution for the system: 3.000000 1.000000 2.000000 01

// method8Solution for the system: 3.000000 1.000000 2.000000 03

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

std;0

Solution for the system: 3.000000 1.000000 2.000000 07

Solution for the system: 3.000000 1.000000 2.000000 6 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>0Solution for the system: 3.000000 1.000000 2.000000 1 Solution for the system: 3.000000 1.000000 2.000000 17// method9#include<bits/stdc++.h>0Solution for the system: 3.000000 1.000000 2.000000 20Solution for the system: 3.000000 1.000000 2.000000 21

// method8// function to reduce matrix to r.e.f. Returns a value to1 #include<bits/stdc++.h>0Solution for the system: 3.000000 1.000000 2.000000 1 Solution for the system: 3.000000 1.000000 2.000000 26

using2// method9#include<bits/stdc++.h>0Solution for the system: 3.000000 1.000000 2.000000 30Solution for the system: 3.000000 1.000000 2.000000 31

// C++ program to demonstrate working of Gaussian Elimination6_______555_______9#include<bits/stdc++.h>0Solution 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 38

Solution for the system: 3.000000 1.000000 2.000000 1 Solution for the system: 3.000000 1.000000 2.000000 2Solution 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_______5

// method8Solution for the system: 3.000000 1.000000 2.000000 52

// method8Solution for the system: 3.000000 1.000000 2.000000 1 Solution for the system: 3.000000 1.000000 2.000000 55

// method8Solution for the system: 3.000000 1.000000 2.000000 1 Solution for the system: 3.000000 1.000000 2.000000 58

// method8Solution for the system: 3.000000 1.000000 2.000000 60

using2____555_______4 #include<bits/stdc++.h>0Solution for the system: 3.000000 1.000000 2.000000 69Solution for the system: 3.000000 1.000000 2.000000 70

Solution for the system: 3.000000 1.000000 2.000000 71______1_______72

// method8Solution for the system: 3.000000 1.000000 2.000000 74

Solution for the system: 3.000000 1.000000 2.000000 75Solution for the system: 3.000000 1.000000 2.000000 76

Solution for the system: 3.000000 1.000000 2.000000 75Solution for the system: 3.000000 1.000000 2.000000 78

// method8____555_______4 Solution for the system: 3.000000 1.000000 2.000000 81

using2____558_______7 Solution for the system: 3.000000 1.000000 2.000000 84Solution for the system: 3.000000 1.000000 2.000000 85

// method8Solution for the system: 3.000000 1.000000 2.000000 87

// method8// method4 Solution for the system: 3.000000 1.000000 2.000000 90

using2Solution for the system: 3.000000 1.000000 2.000000 92

// method8____554_______5

using2____554_______01

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

using2Solution 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>0Solution 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 5

Solution for the system: 3.000000 1.000000 2.000000 6 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>0Solution 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>0Solution 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

// 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 Elimination2Solution 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 unknowns0Solution for the system: 3.000000 1.000000 2.000000 3 #include<bits/stdc++.h>12Solution for the system: 3.000000 1.000000 2.000000 1 #define N 3 // Number of unknowns4Solution 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>0Solution 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 6 Solution for the system: 3.000000 1.000000 2.000000 09Solution for the system: 3.000000 1.000000 2.000000 3 // method47

// method32_______554_______5

// method64// function to reduce matrix to r.e.f. Returns a value to1 #include<bits/stdc++.h>0Solution 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 1 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_______554_______5

// method64____1_______52

// method64Solution for the system: 3.000000 1.000000 2.000000 1 Solution for the system: 3.000000 1.000000 2.000000 55

// method64Solution for the system: 3.000000 1.000000 2.000000 1 #include<bits/stdc++.h>97Solution for the system: 3.000000 1.000000 2.000000 1#include<bits/stdc++.h>99

// method64Solution for the system: 3.000000 1.000000 2.000000 60

// method64// function to reduce matrix to r.e.f. Returns a value to1 #include<bits/stdc++.h>0Solution for the system: 3.000000 1.000000 2.000000 1 using06// method60using08

// method8____555_______4 using11

// method8____554_______5

using14____556_______97Solution for the system: 3.000000 1.000000 2.000000 1using17

using14____557_______19

// method8____559_______0

// method64Solution for the system: 3.000000 1.000000 2.000000 74

// 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 84Solution for the system: 3.000000 1.000000 2.000000 85

// 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 90

// method8Solution for the system: 3.000000 1.000000 2.000000 92

// method64// function to reduce matrix to r.e.f. Returns a value to1 #include<bits/stdc++.h>0Solution for the system: 3.000000 1.000000 2.000000 1 using06// method60using08

// method64____554_______5

// method8using56

using57_______557_______58

using57_______557_______60

// method8Solution 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>0Solution 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 6 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>0Solution 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>0Solution 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_______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>0Solution 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

using2Solution for the system: 3.000000 1.000000 2.000000 001

using2Solution for the system: 3.000000 1.000000 2.000000 003

using2Solution 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 to31Solution for the system: 3.000000 1.000000 2.000000 012

// method8Solution for the system: 3.000000 1.000000 2.000000 014

// method8Solution 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 to08Solution for the system: 3.000000 1.000000 2.000000 022

// C++ program to demonstrate working of Gaussian Elimination6_______559_______66____556_______0Solution 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>0Solution for the system: 3.000000 1.000000 2.000000 037Solution for the system: 3.000000 1.000000 2.000000 038Solution for the system: 3.000000 1.000000 2.000000 039Solution 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;08Solution for the system: 3.000000 1.000000 2.000000 054std;10std;09std;08std;09std;08std;09std;24Solution for the system: 3.000000 1.000000 2.000000 054std;28std;09using95// method37std;09std;32std;09std;34Solution 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 1 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 Elimination2Solution for the system: 3.000000 1.000000 2.000000 3 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

// method8Solution 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

using2Solution for the system: 3.000000 1.000000 2.000000 121_______557_______5#include<bits/stdc++.h>2

// method8using8

using2Solution for the system: 3.000000 1.000000 2.000000 121Solution 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 unknowns0Solution for the system: 3.000000 1.000000 2.000000 3 Solution for the system: 3.000000 1.000000 2.000000 153Solution for the system: 3.000000 1.000000 2.000000 1 #define N 3 // Number of unknowns4Solution 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_______554_______5

// method8Solution for the system: 3.000000 1.000000 2.000000 3 Solution for the system: 3.000000 1.000000 2.000000 172

// method8Solution for the system: 3.000000 1.000000 2.000000 174

// method8Solution 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 6 Solution for the system: 3.000000 1.000000 2.000000 09Solution for the system: 3.000000 1.000000 2.000000 3 Solution for the system: 3.000000 1.000000 2.000000 091

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

// method8// function to reduce matrix to r.e.f. Returns a value to1#include<bits/stdc++.h>0Solution for the system: 3.000000 1.000000 2.000000 1 Solution for the system: 3.000000 1.000000 2.000000 197

using2Solution 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 1 Solution for the system: 3.000000 1.000000 2.000000 2Solution for the system: 3.000000 1.000000 2.000000 3 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_______5

// method8

// method8Solution for the system: 3.000000 1.000000 2.000000 52

// method8Solution for the system: 3.000000 1.000000 2.000000 1 Solution for the system: 3.000000 1.000000 2.000000 55

// method8Solution for the system: 3.000000 1.000000 2.000000 1 #include<bits/stdc++.h>97Solution for the system: 3.000000 1.000000 2.000000 1Solution for the system: 3.000000 1.000000 2.000000 228

// method8

// method8Solution for the system: 3.000000 1.000000 2.000000 60

// method8// function to reduce matrix to r.e.f. Returns a value to1#include<bits/stdc++.h>0Solution for the system: 3.000000 1.000000 2.000000 1 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_______97Solution for the system: 3.000000 1.000000 2.000000 1Solution 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

using2Solution for the system: 3.000000 1.000000 2.000000 254

using2Solution for the system: 3.000000 1.000000 2.000000 256

using2Solution 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 84Solution for the system: 3.000000 1.000000 2.000000 85

using2

using2Solution 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 90

Solution for the system: 3.000000 1.000000 2.000000 71______1_______92

using2

using2____561_______1____556_______0Solution for the system: 3.000000 1.000000 2.000000 1 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 71

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>0Solution for the system: 3.000000 1.000000 2.000000 1 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 71

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 6 Solution for the system: 3.000000 1.000000 2.000000 7Solution for the system: 3.000000 1.000000 2.000000 3 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_______554_______5

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

// method8____554_______56

// method8Solution 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>0Solution for the system: 3.000000 1.000000 2.000000 1 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

// method8Solution 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_______554_______5

// method8Solution for the system: 3.000000 1.000000 2.000000 121Solution for the system: 3.000000 1.000000 2.000000 411// method02

// method8Solution 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 6 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 Elimination2Solution 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 461Solution 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>0Solution 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

// method8Solution for the system: 3.000000 1.000000 2.000000 481

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

// method8// method4 #include<bits/stdc++.h>0Solution for the system: 3.000000 1.000000 2.000000 449// function to reduce matrix to r.e.f. Returns a value to53Solution for the system: 3.000000 1.000000 2.000000 460Solution for the system: 3.000000 1.000000 2.000000 490_______1_______443Solution 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_______7Solution 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 522Solution for the system: 3.000000 1.000000 2.000000 449std;09Solution for the system: 3.000000 1.000000 2.000000 525std;09Solution 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>0Solution for the system: 3.000000 1.000000 2.000000 539 Solution for the system: 3.000000 1.000000 2.000000 540Solution for the system: 3.000000 1.000000 2.000000 539 Solution for the system: 3.000000 1.000000 2.000000 542Solution for the system: 3.000000 1.000000 2.000000 443namespace8Solution for the system: 3.000000 1.000000 2.000000 539Solution for the system: 3.000000 1.000000 2.000000 546

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

// method8Solution for the system: 3.000000 1.000000 2.000000 550 namespace14Solution for the system: 3.000000 1.000000 2.000000 449// function to reduce matrix to r.e.f. Returns a value to53Solution for the system: 3.000000 1.000000 2.000000 525Solution for the system: 3.000000 1.000000 2.000000 490Solution for the system: 3.000000 1.000000 2.000000 539Solution for the system: 3.000000 1.000000 2.000000 557

// method8Solution for the system: 3.000000 1.000000 2.000000 449// function to reduce matrix to r.e.f. Returns a value to53Solution for the system: 3.000000 1.000000 2.000000 525Solution for the system: 3.000000 1.000000 2.000000 490Solution for the system: 3.000000 1.000000 2.000000 539Solution for the system: 3.000000 1.000000 2.000000 564Solution for the system: 3.000000 1.000000 2.000000 449// function to reduce matrix to r.e.f. Returns a value to53Solution for the system: 3.000000 1.000000 2.000000 527Solution for the system: 3.000000 1.000000 2.000000 490Solution for the system: 3.000000 1.000000 2.000000 539Solution for the system: 3.000000 1.000000 2.000000 557

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

std;0

Solution for the system: 3.000000 1.000000 2.000000 07

Solution for the system: 3.000000 1.000000 2.000000 447 Solution for the system: 3.000000 1.000000 2.000000 585Solution 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>0Solution for the system: 3.000000 1.000000 2.000000 525_______1_______597Solution for the system: 3.000000 1.000000 2.000000 525Solution for the system: 3.000000 1.000000 2.000000 599Solution for the system: 3.000000 1.000000 2.000000 443namespace8Solution for the system: 3.000000 1.000000 2.000000 525Solution for the system: 3.000000 1.000000 2.000000 603std;66#include<bits/stdc++.h>0Solution 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>0Solution for the system: 3.000000 1.000000 2.000000 527Solution for the system: 3.000000 1.000000 2.000000 597Solution for the system: 3.000000 1.000000 2.000000 527Solution for the system: 3.000000 1.000000 2.000000 542_______1_______443namespace8Solution for the system: 3.000000 1.000000 2.000000 527Solution 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 to53Solution for the system: 3.000000 1.000000 2.000000 525Solution for the system: 3.000000 1.000000 2.000000 490Solution for the system: 3.000000 1.000000 2.000000 527Solution for the system: 3.000000 1.000000 2.000000 627

// C++ program to demonstrate working of Gaussian Elimination6_______559_______66____556_______0Solution 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 38

Solution for the system: 3.000000 1.000000 2.000000 447 Solution for the system: 3.000000 1.000000 2.000000 636Solution 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>0Solution for the system: 3.000000 1.000000 2.000000 539Solution for the system: 3.000000 1.000000 2.000000 597Solution for the system: 3.000000 1.000000 2.000000 539Solution for the system: 3.000000 1.000000 2.000000 599Solution for the system: 3.000000 1.000000 2.000000 443namespace8Solution for the system: 3.000000 1.000000 2.000000 539Solution for the system: 3.000000 1.000000 2.000000 546

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

// method8Solution for the system: 3.000000 1.000000 2.000000 52

// method8Solution for the system: 3.000000 1.000000 2.000000 660 namespace14Solution for the system: 3.000000 1.000000 2.000000 539namespace8

// method8Solution for the system: 3.000000 1.000000 2.000000 665 namespace14Solution for the system: 3.000000 1.000000 2.000000 449// function to reduce matrix to r.e.f. Returns a value to53Solution for the system: 3.000000 1.000000 2.000000 660Solution for the system: 3.000000 1.000000 2.000000 490Solution for the system: 3.000000 1.000000 2.000000 539Solution for the system: 3.000000 1.000000 2.000000 557

// method8Solution for the system: 3.000000 1.000000 2.000000 60

// method8// function to reduce matrix to r.e.f. Returns a value to1 #include<bits/stdc++.h>0Solution for the system: 3.000000 1.000000 2.000000 525 namespace14Solution for the system: 3.000000 1.000000 2.000000 539Solution for the system: 3.000000 1.000000 2.000000 681Solution for the system: 3.000000 1.000000 2.000000 525 Solution for the system: 3.000000 1.000000 2.000000 599Solution for the system: 3.000000 1.000000 2.000000 443namespace8Solution for the system: 3.000000 1.000000 2.000000 525Solution for the system: 3.000000 1.000000 2.000000 546

using2// method4 #include<bits/stdc++.h>0Solution for the system: 3.000000 1.000000 2.000000 69#include<bits/stdc++.h>0Solution for the system: 3.000000 1.000000 2.000000 449// function to reduce matrix to r.e.f. Returns a value to53_______1_______525Solution for the system: 3.000000 1.000000 2.000000 490Solution for the system: 3.000000 1.000000 2.000000 539Solution for the system: 3.000000 1.000000 2.000000 698Solution 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 namespace14Solution for the system: 3.000000 1.000000 2.000000 449// function to reduce matrix to r.e.f. Returns a value to53Solution for the system: 3.000000 1.000000 2.000000 525Solution for the system: 3.000000 1.000000 2.000000 490Solution for the system: 3.000000 1.000000 2.000000 539Solution for the system: 3.000000 1.000000 2.000000 557

Solution for the system: 3.000000 1.000000 2.000000 306_______1_______660 namespace14Solution for the system: 3.000000 1.000000 2.000000 525namespace8

Solution for the system: 3.000000 1.000000 2.000000 71____559_______0

// method8Solution for the system: 3.000000 1.000000 2.000000 720

// method8Solution for the system: 3.000000 1.000000 2.000000 76

// method8Solution for the system: 3.000000 1.000000 2.000000 78

// method8// method4 Solution for the system: 3.000000 1.000000 2.000000 727Solution for the system: 3.000000 1.000000 2.000000 449// function to reduce matrix to r.e.f. Returns a value to53Solution for the system: 3.000000 1.000000 2.000000 539Solution for the system: 3.000000 1.000000 2.000000 490_______1_______660Solution for the system: 3.000000 1.000000 2.000000 492

using2____558_______7 Solution for the system: 3.000000 1.000000 2.000000 539namespace8Solution for the system: 3.000000 1.000000 2.000000 85

// method8Solution for the system: 3.000000 1.000000 2.000000 87

// method8// method4 #include<bits/stdc++.h>0Solution for the system: 3.000000 1.000000 2.000000 660 Solution for the system: 3.000000 1.000000 2.000000 745Solution for the system: 3.000000 1.000000 2.000000 539// method61

using2#define N 3 // Number of unknowns0Solution for the system: 3.000000 1.000000 2.000000 449_______559_______09Solution for the system: 3.000000 1.000000 2.000000 539std;09Solution 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>0Solution for the system: 3.000000 1.000000 2.000000 525 namespace14Solution for the system: 3.000000 1.000000 2.000000 539 Solution for the system: 3.000000 1.000000 2.000000 762Solution for the system: 3.000000 1.000000 2.000000 525 Solution for the system: 3.000000 1.000000 2.000000 599Solution for the system: 3.000000 1.000000 2.000000 443namespace8Solution for the system: 3.000000 1.000000 2.000000 525Solution for the system: 3.000000 1.000000 2.000000 546

// method8____554_______5

using2____554_______01

using2____554_______03

using2Solution for the system: 3.000000 1.000000 2.000000 776 namespace14_______1_______449// function to reduce matrix to r.e.f. Returns a value to53Solution for the system: 3.000000 1.000000 2.000000 525Solution for the system: 3.000000 1.000000 2.000000 490Solution for the system: 3.000000 1.000000 2.000000 539Solution for the system: 3.000000 1.000000 2.000000 783Solution for the system: 3.000000 1.000000 2.000000 449// function to reduce matrix to r.e.f. Returns a value to53Solution for the system: 3.000000 1.000000 2.000000 539Solution for the system: 3.000000 1.000000 2.000000 490Solution 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>0Solution for the system: 3.000000 1.000000 2.000000 527 namespace14Solution for the system: 3.000000 1.000000 2.000000 539 Solution for the system: 3.000000 1.000000 2.000000 762Solution for the system: 3.000000 1.000000 2.000000 527 Solution for the system: 3.000000 1.000000 2.000000 542Solution for the system: 3.000000 1.000000 2.000000 443namespace8Solution for the system: 3.000000 1.000000 2.000000 527Solution 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 to53Solution for the system: 3.000000 1.000000 2.000000 525Solution for the system: 3.000000 1.000000 2.000000 490Solution for the system: 3.000000 1.000000 2.000000 527Solution for the system: 3.000000 1.000000 2.000000 813Solution for the system: 3.000000 1.000000 2.000000 449// function to reduce matrix to r.e.f. Returns a value to53Solution for the system: 3.000000 1.000000 2.000000 539Solution for the system: 3.000000 1.000000 2.000000 490Solution for the system: 3.000000 1.000000 2.000000 527Solution for the system: 3.000000 1.000000 2.000000 819Solution for the system: 3.000000 1.000000 2.000000 776namespace8

using2____554_______19

using2Solution for the system: 3.000000 1.000000 2.000000 449// function to reduce matrix to r.e.f. Returns a value to53Solution for the system: 3.000000 1.000000 2.000000 525Solution for the system: 3.000000 1.000000 2.000000 490Solution for the system: 3.000000 1.000000 2.000000 539Solution for the system: 3.000000 1.000000 2.000000 830

// method8____559_______0

// method8Solution 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 5

Solution for the system: 3.000000 1.000000 2.000000 447 Solution for the system: 3.000000 1.000000 2.000000 845Solution 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 namespace14Solution for the system: 3.000000 1.000000 2.000000 856Solution for the system: 3.000000 1.000000 2.000000 857Solution for the system: 3.000000 1.000000 2.000000 443Solution 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>0Solution for the system: 3.000000 1.000000 2.000000 525 namespace14Solution for the system: 3.000000 1.000000 2.000000 443 Solution for the system: 3.000000 1.000000 2.000000 871Solution for the system: 3.000000 1.000000 2.000000 525 Solution for the system: 3.000000 1.000000 2.000000 873Solution for the system: 3.000000 1.000000 2.000000 525Solution for the system: 3.000000 1.000000 2.000000 875

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

// method8____554_______56

// method8Solution for the system: 3.000000 1.000000 2.000000 854// function to reduce matrix to r.e.f. Returns a value to53_______1_______525Solution for the system: 3.000000 1.000000 2.000000 564Solution for the system: 3.000000 1.000000 2.000000 449// function to reduce matrix to r.e.f. Returns a value to53Solution for the system: 3.000000 1.000000 2.000000 525Solution for the system: 3.000000 1.000000 2.000000 490Solution for the system: 3.000000 1.000000 2.000000 443Solution 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>0Solution for the system: 3.000000 1.000000 2.000000 527 namespace14Solution for the system: 3.000000 1.000000 2.000000 525 Solution for the system: 3.000000 1.000000 2.000000 762Solution for the system: 3.000000 1.000000 2.000000 527 Solution for the system: 3.000000 1.000000 2.000000 599Solution for the system: 3.000000 1.000000 2.000000 443namespace8Solution for the system: 3.000000 1.000000 2.000000 527Solution for the system: 3.000000 1.000000 2.000000 546

// method8____554_______5

using2____554_______71

using2____554_______73

using2____554_______75

using2Solution for the system: 3.000000 1.000000 2.000000 854// function to reduce matrix to r.e.f. Returns a value to53Solution for the system: 3.000000 1.000000 2.000000 525Solution for the system: 3.000000 1.000000 2.000000 813Solution for the system: 3.000000 1.000000 2.000000 449// function to reduce matrix to r.e.f. Returns a value to53Solution for the system: 3.000000 1.000000 2.000000 525Solution for the system: 3.000000 1.000000 2.000000 490Solution for the system: 3.000000 1.000000 2.000000 527Solution for the system: 3.000000 1.000000 2.000000 819Solution for the system: 3.000000 1.000000 2.000000 854// function to reduce matrix to r.e.f. Returns a value to53Solution 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

// method8Solution for the system: 3.000000 1.000000 2.000000 854// function to reduce matrix to r.e.f. Returns a value to53Solution for the system: 3.000000 1.000000 2.000000 525Solution for the system: 3.000000 1.000000 2.000000 564Solution for the system: 3.000000 1.000000 2.000000 854// function to reduce matrix to r.e.f. Returns a value to53Solution for the system: 3.000000 1.000000 2.000000 525Solution for the system: 3.000000 1.000000 2.000000 945Solution for the system: 3.000000 1.000000 2.000000 449// function to reduce matrix to r.e.f. Returns a value to53Solution for the system: 3.000000 1.000000 2.000000 525Solution for the system: 3.000000 1.000000 2.000000 490Solution 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>0Solution for the system: 3.000000 1.000000 2.000000 525 Solution for the system: 3.000000 1.000000 2.000000 540Solution for the system: 3.000000 1.000000 2.000000 525 Solution for the system: 3.000000 1.000000 2.000000 599Solution for the system: 3.000000 1.000000 2.000000 443namespace8Solution for the system: 3.000000 1.000000 2.000000 525Solution for the system: 3.000000 1.000000 2.000000 546

// method8std;66Solution for the system: 3.000000 1.000000 2.000000 972Solution for the system: 3.000000 1.000000 2.000000 973#include<bits/stdc++.h>0Solution for the system: 3.000000 1.000000 2.000000 854// function to reduce matrix to r.e.f. Returns a value to53Solution for the system: 3.000000 1.000000 2.000000 525Solution for the system: 3.000000 1.000000 2.000000 978Solution 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; .

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Ví dụ loại bỏ Gaussian là gì?

Loại bỏ Gaussian là ref hay rref?

Thuật toán loại bỏ Gaussian là gì?

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