Answer
$\left[\begin{array}{c}
{-16}\\
{7}\\
{-4}\\
{7}\end{array}\right]$
Work Step by Step
If $A$ is an $m\times\boxed{n }$ matrix and $B$ is an $\boxed{n }\times k$ matrix,
then the product $AB$ is the $m\times k$ matrix whose $ij-$th entry is the product
$(AB)_{ij}=[a_{i1}\ a_{i2}\ a_{i3}\ \ldots\ a_{in}]\left[\begin{array}{l}
b_{1j}\\
b_{2j}\\
b_{3j}\\
\vdots\\
b_{nj}
\end{array}\right]$
$=a_{i1}b_{1j}+a_{i2}b_{2j}+a_{i3}b_{3j}+\cdots+a_{in}b_{nj}$.
-------
Here,
A is a $4\times 4$ matrix, B is a $4\times 1$ matrix
AB is defined, and is a $4\times 1$ matrix.
$AB=\left[\begin{array}{c}
{1 \cdot 1+1 \cdot(-3)+(-7) \cdot 2+0 \cdot 1}\\
{(-1)\cdot 1+0\cdot(-3)+2\cdot 2+4\cdot 1}\\
{(-1)\cdot 1+0\cdot(-3)+(-2)\cdot 2+1\cdot 1}\\
{1\cdot 1+(-1)(-3)+1\cdot 2+1\cdot 1}\end{array}\right]=$$\left[\begin{array}{c}
{-16}\\
{7}\\
{-4}\\
{7}\end{array}\right]$