Write a MATLAB function that solves a system of linear equations or calculates t

Question

Write a MATLAB function that solves a system of linear equations or calculates the inverse of a matrix by Gauss-Jordan elimination- Your function should accept a matrix as an argument and return a matrix of the same dimension. Note: Your function should be written to handle matrices of any size. Use variable names that relate to their function and include comments that explain your program logic Do not use any built-in MATLAB functions except size(), input(), and zeros(). As example of what is expected from this function consider the following linear system: 3x + 2y + z = 11 2x + 3y + z = 13 x + y + 4z = 12 In this case you should pass into your function the following augmented matrix: (3 2 1 11 2 3 1 13 1 1 4 12) After performing Gauss-Jordan elimination, your function should return the following reduced system: (1 0 0 1 0 1 0 3 0 0 1 2) from which we can determine that x = 1, y = 3, z = 2. Furthermore, if you pass a double augmented matrix such as (3 2 1 11 -5 2 3 1 13 -4 1 1 4 12 9) Your function should return (1 0 0 1 -2 0 1 0 3 -1 0 0 1 2 3) which solve the original equations 3x + 2y + z = 11 2x + 3y + z = 13 x + y + 4z = 12 as x = 1, y = 3, z = 2 and; at the same time, the equations 3x + 2y + z = -5 2x + 3y + z = -4 x + y + 4z = 9 as x = -2, y = -1, z = 3.

Explanation / Answer

function [y]=gauss_jordan(A)
a=A;
[m n]=size(A);
for i=1:m-1
if a(i,i)==0
  
flag=0;
j=i+1;
while flag==0 && j<=m
if a(j,i)~=0
flag=1;
temp=a(j,:);
a(j,:)=a(i,:);
a(i,:)=temp;
end
end
end
end
  

for i=1:m
for j=1:m
if j==i || a(j,i)==0
continue;
else
ratio=a(i,i)/a(j,i);
a(j,:)=a(i,:)-ratio*a(j,:);
end
end

end

for i=1:m
a(i,:)=a(i,:)/a(i,i);
end
y=a;
end

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