If $\begin{pmatrix} a+4 &3b \\ 8 & -6 \end{pmatrix} = \begin{pmatrix} 2a+2 &b+2 \\ 8 & a-8b \end{pmatrix}$, write the value of $a-2b$.

Answer 1

If $\begin{pmatrix} a+4 &3b \\ 8 & -6 \end{pmatrix} = \begin{pmatrix} 2a+2 &b+2 \\ 8 & a-8b \end{pmatrix}$:

$\Rightarrow a + 4 = 2a + 2 \rightarrow a = 2$

$\Rightarrow 3b = b+2 \rightarrow b = 1$

$\Rightarrow a - 2b = 2 - 2 \times 1 = 0$