If $\begin{bmatrix} 1 & 2 \ 3 & 3 \end{bmatrix} \begin{bmatrix} x & 0 \ 0 & y \end{bmatrix} = \begin{bmatrix} x & 0 \ 9 & 0 \end{bmatrix}$, find the values of x and y.

$\Rightarrow \begin{bmatrix} 1 & 2 \ 3 & 3 \end{bmatrix} \times \begin{bmatrix} x & 0 \ 0 & y \end{bmatrix} = \begin{bmatrix} x & 0 \ 9 & 0 \end{bmatrix} \\[1em] \Rightarrow \begin{bmatrix} (1)(x) + (2)(0) & (1)(0) + (2)(y) \ (3)(x) + (3)(0) & (3)(0) + (3)(y) \end{bmatrix} = \begin{bmatrix} x & 0 \ 9 & 0 \end{bmatrix} \\[1em] \Rightarrow \begin{bmatrix} x + 2 & 2y \ 3x & 3y \end{bmatrix} = \begin{bmatrix} x & 0 \ 9 & 0 \end{bmatrix}$

Solving for x and y:

∴ 3x = 9

⇒ x = $\dfrac{9}{3}$

⇒ x = 3.

∴ 2y = 0

⇒ y = 0.

Hence, x = 3 and y = 0.