Let \(\mathbf{A}\) be a matrix such that \(\mathbf{A}^{-1} = \begin{pmatrix} 1 & 1 \\ 2 & x \end{pmatrix}\) for some value of \(x \). What is the vector that \(\mathbf{A}\) maps to \(\begin{pmatrix} 1 \\ 0 \end{pmatrix}?\)
The answer is \(\begin{pmatrix} 3 \\ -7 \end{pmatrix}\).
