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!!!

Printable View

- Jan 29th 2007, 11:12 AMTreeMoneyMatrix Product
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!!! - Jan 29th 2007, 03:48 PMtopsquark
I would consider this to be more of a definition than something that needs to be proved.

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

Then by the definition of matrix multiplication:

$\displaystyle C_{mn} \equiv \sum_{j} A_{mj}B_{jn}$

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

-Dan