Augmented matrix with symbolic variables and rref-CodePudding

Take a look at

syms x y z
A=[1 -2 x;2 1 y;-3 1 z]
rref(A)

This is an augmented matrix and I need the final output to be

1  0  | (x 2y)/5
0  1  | (y-2x)/5
0  0  | z x y

But rref() yeilds this

1  0  0
0  1  0
0  0  1

Any suggestions how to get the intended output?

CodePudding user response：

As long as the symbolic variables are confined to the right half of your augmented matrix, you could proceed as follows. Suppose that [A|B] is your augmented matrix. Then, you could do the following.

M = rref([A, eye(size(A,1))]);
C = M(:,(size(A,2) 1):end) * B;

In this case, C is the result of applying the row operations that brought M to its RREF to the symbolic matrix B.

Here's a modification that produces the result you initially expected.

syms x y z
A=[1 -2;2 1;-3 1];
B=[x;y;z];

[m,n] = size(A);
M = [eye(m),zeros(m,n)];
M(:,1:n) = A;
M(:,(m 1):end) = eye(m,n);
P = M(:,n 1:end);

R = rref(M);
C = R(:,n 1:end)/P*B;

disp(C)

Result:

 x/5   (2*y)/5
 y/5 - (2*x)/5
     x   y   z