In the expression
\(\begin{bmatrix} 1 & 2 \\ -1 & 0 \\ 3 & 1\end{bmatrix}
\begin{bmatrix} -2 & 1 \\ 0 & 1\end{bmatrix}
= \begin{bmatrix}
-2 & 3 \\
x & -1 \\
-6 & 4 \\
\end{bmatrix}\).
What is \(x\)?
The answer is 2.
Recall that the first column of the product is
given by
\(\begin{bmatrix} 1 & 2 \\ -1 & 0 \\ 3 & 1\end{bmatrix}
\begin{bmatrix} -2 \\ 0 \end{bmatrix}
=
\begin{bmatrix} 1(-2) + 2(0) \\ -1(-2) + 0(0) \\ 3(-2) + 1(0) \end{bmatrix}
=
\begin{bmatrix} -2 \\ 2 \\ -6\end{bmatrix}.
\)