Answer
$$
\begin{bmatrix}
-3 \\
1 \\
-4
\end{bmatrix}
$$
Work Step by Step
Our task is to compute this product:
$$
\begin{bmatrix}
6 & 5 \\
-4 & -3 \\
7 & 6
\end{bmatrix}
\begin{bmatrix}
2 \\ -3
\end{bmatrix}
$$
By the definition of matrix-vector multiplication, we simplify it to this form:
$$
\begin{bmatrix}
6(2) + 5(-3) \\
-4(2) -3(-3) \\
7(2) + 6(-3)
\end{bmatrix}
$$
And through basic arithmetic, the expression boils down to
$$
\begin{bmatrix}
-3 \\
1 \\
-4
\end{bmatrix}
$$
