"Compute (B^T)(C) and multiply the result by A on the right"

nietzsche

1. The problem statement, all variables and given/known data

I have three 3x1 matrices A, B, and C.

First I have to multiply (AB^T)C. I understand the result is a 3x1 matrix (I think).

Next the question says "Compute (B^T)C and multiply the result by A on the right. (Hint: (B^T)C is 1x1).

The last question is "Explain why (AB^T)C = ((B^T)C)A.

2. Relevant equations



3. The attempt at a solution

I don't understand the second question. Does "multiply the result by A on the right" mean ((B^T)C)A or A((B^T)C)? Because I find that the former is not defined but the latter is.

But then I got confused because of the last question.

Can anyone clarify this for me? I'd appreciate it, thanks.

D H

Multiply X on the right by Y means XY, not YX. As you have discovered, matrix multiplication is not commutative. It is transitive, however.

nietzsche

Thanks a lot!