© December 2019 | IJIRT | Volume 6 Issue 7 | ISSN: 2349-6002 IJIRT 148839 INTERNATIONAL JOURNAL OF INNOVATIVE RESEARCH IN TECHNOLOGY 75 Gauss Jordan Method to Obtain Solution of Simultaneous Equation Vishal Vaman Mehtre 1 , Aakriti 2 1 Assistant Professor, Department of Electrical Engineering BVDUCOE, Pune, India 2 Student, Department of Electrical, Engineering, BVDUCOE, Pune, India Abstract- The review paper consists of GAUSS JORDAN METHOD using MATLAB to solve simultaneous algebraic equations by row and column elimination. In MATLAB there is a proper set of codes that is given as input, and the desired output result is obtained. The GAUSS JORDAN METHOD is also used for solving of simultaneous algebraic equations. The augmented matrix is reduced to echelon form and then the desired result is obtained 1. INTRODUCTION The GAUSS ELIMINATION Method is named after Mathematician Carl Friedrich Gauss and Wilhelm Jordan, after their Name It Is Called So. It is a Technique in Which A System of Linear Equations Is Resolved By Means Of Matrices.[6] 2.GAUSS JORDAN METHOD Gauss Jordan method is a method to solve linear simultaneous algebraic equations. This method involves transformation of rows and columns to reduce the matrix into echelon form. Gauss Jordan method is also useful in finding inverse of a matrix. Solve the following system of equations using GAUSS JORDAN METHOD.[2] { x+2yz+3v+w=2, 2x+4y-2z+6v+3w=6, -x2y+zv+3w=4}? It is a system of 3 equations in 5 variables. So, there are not any unique solutions. The most we can do is get 3 linear independent equations.in this case the equations are actually very similar , if we multiply the first equations by 2 and subtract it from the second equation , we get w=2 .if we add the first and third equations , we get 2v+4w=6. Substituting w=2 gives us v= -1. This just leaves us with x+2y-z=3. That’s all we can find out from the given in this method: Information. 3. GAUSS JORDAN METHOD IN MATLAB. CODE Gauss Jordan Method MATLAB Function[X,err]=gauss_jordan_elim(a,b) [2] D = [0 2 1; 1 1 2; 2 1 1] [3] E= [4; 6; 7] 4 [1] [a,b]=size(D); 5 err =0; 6 X=zeros(a,1);. 7 if ~= a b 8 disp('error: a~=b'); 9 err = 1; 10 end 11 if length(E) ~= a 12 disp('error: wrong size of E'); 13 err = 2; 14 else 15 if size(E,2) ~= 1 16 E=E'; 17 end 18 if size(E,2) ~= 1 19 disp('error: E is a matrix'); 20 err = 3; 21 end 22 end 23 if err == 0 24 A=[D,E]; 25 for i=1:a 26 [A (i:a,i:a+1),err]=gauss_pivot(A(i:a,i:a+1)); 27 if err == 0 28 A(1:a,i:a+1)=gauss_jordan_step(A(1:a,i:a+ 1),i); 29 end 30 end 31 x=A(:,a+1); 32 end 33 D=0; 34 function A1=gauss_jordan_step(D,i) 35 36 [a,b]=size(D); 37 D1=D; 38 S=D1(i,1); 39 D1(i,:) = D(i,:)/S; 40 k=[[1:i-1],[i+1:a]]; 41 for j=k 42 S=D1(j,1); 43 D1(j,:)=D1(j,:)D1(i,:)*S; 44 end 45 function [D1, err]=gauss_pivot(D) 46 [a,b]=size(D);. 47 D1=D; 48 err = 0; % error flag 49 if D1 (1,1) == 0 50 check= logical(1);. 51 i = 1; 52 while check 53 i = i + 1; 54 if i > a 55 disp('error: matrix is singular'); 56 err = 1; 57 check = logical(0); 58 else 59 if D(i,1) ~= 0 & check 60 check = logical(0); 61 E=E1(i,:); 62 D1(i,:)=D1(1,:); 63 D1(1,:)=E; 764 end 65 end 66 end 67 end The given program code is for solving the following equations using Gauss Jordan method in MATLAB: 0x + 2y + 1z = 4 1x + 1y + 2z = 6 2x + 1y+ 1z = 7 Therefore in the program, the value of A = [0 2 1;1 1 2; 2 1 1] and that of B = [4;6;7]. In order to run the program, use the