If $\begin{bmatrix$}[r] 8 & 0 \ 0 & 8 \end{bmatrix}\begin{bmatrix}[r] x \ y \end{bmatrix} = \begin{bmatrix}[r] 24 \ -24 \end{bmatrix} then the values of x and y are :

1. x = 3, y = -3

2. x = 48, y = 0

3. x = 0, y = 48

4. x = 16, y = -32

Given,

$\Rightarrow \begin{bmatrix$}[r] 8 & 0 \ 0 & 8 \end{bmatrix}\begin{bmatrix}[r] x \ y \end{bmatrix} = \begin{bmatrix}[r] 24 \ -24 \end{bmatrix} \\[1em] \Rightarrow \begin{bmatrix}[r] 8 \times x + 0 \times y \ 0 \times x + 8 \times y \end{bmatrix} = \begin{bmatrix}[r] 24 \ -24 \end{bmatrix} \\[1em] \Rightarrow \begin{bmatrix}[r] 8x \ 8y \end{bmatrix} = \begin{bmatrix}[r] 24 \ -24 \end{bmatrix} \\[1em] \Rightarrow \begin{bmatrix}[r] x \ y \end{bmatrix} = \dfrac{1}{8}\begin{bmatrix}[r] 24 \ -24 \end{bmatrix} \\[1em] \Rightarrow \begin{bmatrix}[r] x \ y \end{bmatrix} = \begin{bmatrix}[r] 3 \ -3 \end{bmatrix}.

∴ x =3, y = -3.

Hence, Option 1 is the correct option.