Question

Using \[X=A^{-1}B\] for \[2x+5y=1\] and \[3x+2y=7\], what is \[X\]?

Options

• \[\begin{bmatrix}3\\-1\end{bmatrix}\]

• \[\begin{bmatrix}-3\\1\end{bmatrix}\]

• \[\begin{bmatrix}7\\1\end{bmatrix}\]

• \[\begin{bmatrix}1\\3\end{bmatrix}\]

Answer 1

Multiplication gives \[X=-\frac1{11}\begin{bmatrix}-33\\11\end{bmatrix}=\begin{bmatrix}3\\-1\end{bmatrix}.\] Therefore, \(x=3\) and \(y=-1\).