//reduce the matrix to row echelon form
clear;
A=[2,-1,3,2;1,4,0,-1;2,6,-1,5]
disp(A,"A:")
disp("Applying row transformations")
disp("R1=R1-2*R2");
A(1,:)=A(1,:)-2*A(2,:);
disp(A,"A:")
disp("R3=R3-2*R2");
A(3,:)=A(3,:)-2*A(2,:);
disp(A,"A:")
disp("R3=R3//(-2)");
A(3,:)=(-1/2)*A(3,:);
disp(A,"A:")
disp("R2=R2-4*R3");
A(2,:)=A(2,:)-4*A(3,:);
disp(A,"A:")
disp("R1=R1+9*R3");
A(1,:)=A(1,:)+9*A(3,:);
disp(A,"A:")
disp("R1=R1*2/15");
A(1,:)=A(1,:)*2/15;
disp(A,"A:")
disp("R2=R2+2*R1");
A(2,:)=A(2,:)+2*A(1,:);
disp(A,"A:")
disp("R3=R3-R1/2");
A(3,:)=A(3,:)-1/2*A(1,:);
disp(A,"A:")
x=A(1,:);
A(1,:)=A(2,:)
A(2,:)=x
y=A(2,:)
A(2,:)=A(3,:)
A(3,:)=y
disp(A,"A:");