[tex]\begin{bmatrix}9&-5\end{bmatrix}\begin{bmatrix}4&-2\\3&9\end{bmatrix}=\begin{bmatrix}\begin{bmatrix}9&-5\end{bmatrix}\begin{bmatrix}4\\3\end{bmatrix}&\begin{bmatrix}9&-5\end{bmatrix}\begin{bmatrix}-2\\9\end{bmatrix}\end{bmatrix}[/tex]
Basically the row vector on the left can be distributed along the columns of the right matrix. Then computing the product of the row with each column is essentially taking the dot product of two vectors:
[tex]=\begin{bmatrix}9(4)+(-5)(3)&9(-2)+(-5)(9)\end{bmatrix}[/tex]
[tex]=\begin{bmatrix}21&-63\end{bmatrix}[/tex]
