If $\begin{bmatrix$}[r] 2 & 0 \ 0 & 4 \end{bmatrix}\begin{bmatrix}[r] x \ y \end{bmatrix} = \begin{bmatrix}[r] 2 \ -8 \end{bmatrix}, the values of x and y respectively are :

1. 1, -2

2. -2, 1

3. 1, 2

4. -2, -1

Solving,

$\Rightarrow \begin{bmatrix$}[r] 2 & 0 \ 0 & 4 \end{bmatrix}\begin{bmatrix}[r] x \ y \end{bmatrix} = \begin{bmatrix}[r] 2 \ -8 \end{bmatrix} \\[1em] \Rightarrow \begin{bmatrix}[r] 2.x + 0.y \ 0.x + 4.y \end{bmatrix} = \begin{bmatrix}[r] 2 \ -8 \end{bmatrix} \\[1em] \Rightarrow \begin{bmatrix}[r] 2x + 0 \ 0 + 4y \end{bmatrix} = \begin{bmatrix}[r] 2 \ -8 \end{bmatrix} \\[1em] \Rightarrow \begin{bmatrix}[r] 2x \ 4y \end{bmatrix} = \begin{bmatrix}[r] 2 \ -8 \end{bmatrix} \\[1em] \Rightarrow 2x = 2 \text{ and } 4y = -8 \\[1em] \Rightarrow x = \dfrac{2}{2} \text{ and } y = -\dfrac{8}{4} \\[1em] \Rightarrow x = 1 \text{ and } y = -2.

Hence, Option 1 is the correct option.