Matrix Product

Quote:

Originally Posted by TreeMoney

Show that the jth column of the matrix product AB is equal to the matrix product ABj, where Bj is the jth column of B.

I know this is true, but I'm not sure how to show it. Could someone please help me out? TIA!!!

I would consider this to be more of a definition than something that needs to be proved.

Let $[A_{ij}]$ and $[B_{jk}]$ be your matrices.

Then by the definition of matrix multiplication:
$C_{mn} \equiv \sum_{j} A_{mj}B_{jn}$

So the jth column vector in C is $C_j = AB_j$ by definition.

-Dan