Question

Calculate a23 for the product of the following matrices

Answer 1

If $A$ is the matrix product

$A=\underbrace{\begin{pmatrix}1&2\\4&3\end{pmatrix}}_{M_1}\underbrace{\begin{pmatrix}6&1&5\\7&3&4\end{pmatrix}}_{M_2}$

and $a_{2,3}$ is the entry of $A$ in the second row and third column, then

$a_{2,3}=\begin{pmatrix}4&3\end{pmatrix}\begin{pmatrix}5\\4\end{pmatrix}=4\times5+3\times4=\boxed{32}$

That is, the 2nd row, 3rd column entry of $A$ is the product of the 2nd row of $M_1$ and the 3rd column of $M_2$.