taiwan-gsat 2023 Q2

taiwan-gsat · Other · gsat__math-b 5 marks Matrices Matrix Algebra and Product Properties
Consider a real $2 \times 2$ matrix $\left[ \begin{array} { l l } a & b \\ c & d \end{array} \right]$. If $\left[ \begin{array} { l l } 0 & 1 \\ 1 & 0 \end{array} \right] \left[ \begin{array} { l l } a & b \\ c & d \end{array} \right] \left[ \begin{array} { c c } 1 & 0 \\ 0 & - 2 \end{array} \right] = \left[ \begin{array} { c c } 3 & - 4 \\ - 9 & - 7 \end{array} \right]$, what is the value of $c - 2b$?
(1) $- 11$ (2) $- 4$ (3) $1$ (4) $10$ (5) $11$
Consider a real $2 \times 2$ matrix $\left[ \begin{array} { l l } a & b \\ c & d \end{array} \right]$. If $\left[ \begin{array} { l l } 0 & 1 \\ 1 & 0 \end{array} \right] \left[ \begin{array} { l l } a & b \\ c & d \end{array} \right] \left[ \begin{array} { c c } 1 & 0 \\ 0 & - 2 \end{array} \right] = \left[ \begin{array} { c c } 3 & - 4 \\ - 9 & - 7 \end{array} \right]$, what is the value of $c - 2b$?

(1) $- 11$
(2) $- 4$
(3) $1$
(4) $10$
(5) $11$