If $x\begin{bmatrix} 3 \\ 1 \end{bmatrix} + y\begin{bmatrix} 2 \\ -1 \end{bmatrix} = \begin{bmatrix} 12 \\ -1 \end{bmatrix}$, what is $xy$?

Explanation

1. 01

   Equating rows: $3x + 2y = 12$ and $x - y = -1$.

2. 02

   Then $x = y - 1$, so $3y - 3 + 2y = 12$, $y = 3$ and $x = 2$. So $xy = 6$.