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Question
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.
Solution
\[\begin{pmatrix}a + 4 & 3b \\ 8 & - 6\end{pmatrix} = \begin{pmatrix}2a + 2 & b + 2 \\ 8 & a - 8b\end{pmatrix}\]
\[\Rightarrow a + 4 = 2a + 2, 3b = b + 2 \text { and } - 6 = a - 8b\]
⇒ a = 2 and b = 1
∴ a − 2b = 2 − 2(1) = 0
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