Matrix Properties

In the expression

2 [\begin{matrix} - 1 & 0 \\ 2 & - 2 \end{matrix}] - [\begin{matrix} 1 & 2 \\ 4 & 3 \end{matrix}] = [\begin{matrix} - 3 & a \\ 0 & b \end{matrix}]

, what is

a - b

The answer is 5.

Note that $2 [\begin{matrix} - 1 & 0 \\ 2 & - 2 \end{matrix}] - [\begin{matrix} 1 & 2 \\ 4 & 3 \end{matrix}] = [\begin{matrix} - 2 & 0 \\ 4 & - 4 \end{matrix}] + [\begin{matrix} - 1 & - 2 \\ - 4 & - 3 \end{matrix}] = [\begin{matrix} (- 2) + (- 1) & 0 + (- 2) \\ 4 + (- 4) & (- 4) + (- 3) \end{matrix}] = [\begin{matrix} - 3 & - 2 \\ 0 & - 7 \end{matrix}]$ .

Therefore, $a = - 2$ and $b = - 7$ and $a - b = - 2 - (- 7) = - 2 + 7 = 5$ .

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