Let's solve the given matrix equation:

$\begin{bmatrix} 2 & 3 \\ -1 & 2 \end{bmatrix} \begin{bmatrix} x \\ 6 \end{bmatrix} = \begin{bmatrix} 20 \\ y \end{bmatrix}$

To find $x$ and $y$, we will multiply the matrices on the left side:

1. The first equation comes from the first row: $2x + 3(6) = 20$ $2x + 18 = 20$ $2x = 2$ $x = 1$

2. The second equation comes from the second row: $-1x + 2(6) = y$ $-1(1) + 12 = y$ $y = 11$

Therefore, the values are: $x = 1, \quad y = 11$

Would you like more details or have any further questions?

Here are some related questions to deepen your understanding:

1. How do we multiply two matrices of different dimensions?
2. What conditions need to be met for two matrices to be multiplied?
3. How can matrix equations be used to solve systems of linear equations?
4. What is the inverse of a matrix, and how is it used to solve matrix equations?
5. Can matrix operations be applied in solving real-world problems? If yes, how?

Tip: When solving matrix equations, always ensure that the dimensions match for multiplication. For instance, an $m \times n$ matrix can be multiplied by an $n \times p$ matrix.