Solving for unknown matrix X

Solve matrix equation AXB=C, solve for matrix X

Hey. Can some of you help me with this task? I've tried multiple ways to solve this but I just can't figure out how to solve for the unknown matrix X.

Image inserted.

Thank you.

Answer 1

[Hiro Yoshino]

I would use a pesudoinverse:

A = [6 4;6 1; 1 2; 6 4]

A = 4×2

6 4 6 1 1 2 6 4

B = [8 8 6 7 5; 8 8 1 6 0; 1 4 3 8 7]

B = 3×5

8 8 6 7 5 8 8 1 6 0 1 4 3 8 7

C = [18042 21288 10716 22446 12924; 12768 15024 7593 15795 9099;...
    5351 6332 3174 6697 3854; 18042 21288 10716 22446 12924]

C = 4×5

18042 21288 10716 22446 12924 12768 15024 7593 15795 9099 5351 6332 3174 6697 3854 18042 21288 10716 22446 12924

How about thinking of Moore-Penrose pseudoinverse?

X =  pinv(A)*C*pinv(B)

X = 2×3

111.0000 105.0000 107.0000 101.0000 105.0000 110.0000

Check if this works well:

A*X*B - C

ans = 4×5

1.0e-10 * 0.1091 0.1091 0.0364 0.1091 0.0364 0.1091 0.1273 0.0364 0.1091 0.0364 0.0182 0.0182 0.0091 0.0182 0.0045 0.1091 0.1091 0.0364 0.1091 0.0364

Floating-point relative accuracy is given by

eps

ans = 2.2204e-16