In the expression
\(
2\begin{bmatrix} -1 & 0\\ 2 & -2\end{bmatrix}
-\begin{bmatrix} 1 & 2 \\ 4 & 3\end{bmatrix}
=
\begin{bmatrix} -3 & a \\ 0 & b\end{bmatrix}\),
what is \(a - b\)?
The answer is 5.
Note that
\(
2\begin{bmatrix} -1 & 0\\ 2 & -2\end{bmatrix}
-\begin{bmatrix} 1 & 2 \\ 4 & 3\end{bmatrix}
=
\begin{bmatrix} -2 & 0\\ 4 & -4\end{bmatrix}
+\begin{bmatrix} -1 & -2 \\ -4 & -3\end{bmatrix}
= \begin{bmatrix} (-2)+(-1) & 0+(-2) \\ 4+(-4) & (-4)+(-3)\end{bmatrix}
= \begin{bmatrix} -3 & -2 \\ 0 & -7\end{bmatrix}\).
Therefore, \(a = -2\) and \(b = -7\) and \(a - b = -2 - (-7) = -2 + 7 = 5\).