Matrix multiplication - Express a column as a linear combination Let $A = \begin{bmatrix}
3 & -2 & 7\\ 
6 & 5 & 4\\ 
0 & 4 & 9
\end{bmatrix} $ and  $B = \begin{bmatrix}
6 & -2 & 4\\ 
0 & 1 & 3\\ 
7 & 7 & 5
\end{bmatrix} $
Express the third column matrix of $AB$ as a linear combination of the column matrices of $A$
I don't get this... surely the 3rd column would be an expression of the row matrices of $A$ since the 3rd column of$AB$ would be $
\begin{bmatrix}
3(4) & -2(3) & 7(5)\\ 
6(4) & 5(3) & 4(5)\\ 
0(4) & 4(3) & 9(5)
\end{bmatrix} $
As I typed out the question I see my answer...
the 3rd column is $4\begin{bmatrix}
3\\ 
6\\ 
0
\end{bmatrix} 3 \begin{bmatrix}
-2\\ 
5\\ 
4
\end{bmatrix} 5 \begin{bmatrix}
7\\ 
4\\ 
9
\end{bmatrix}$
Is this correct?

The third column of $AB$ is $$A\begin{bmatrix}
4\\ 
3\\ 
5
\end{bmatrix}$$
and if we denote the columns of $A=[C_1 C_2 C_3]$ then the third column of $AB$ is
 $$A\begin{bmatrix}
4\\ 
3\\ 
5
\end{bmatrix}=[C_1 C_2 C_3]\begin{bmatrix}
4\\ 
3\\ 
5
\end{bmatrix}=4C_1+3C_2+5C_3$$
