Let
Find vectors
in \(\mathbb{R}^2\) such that \(S\) is the transition matrix from the basis \({v_1, v_2}\) to the basis \({w_1, w_2}\).
\(v_1 = \begin{bmatrix} -7 \\ 1 \end{bmatrix}\), \(v_2 = \begin{bmatrix} 1 \\ -4 \end{bmatrix}\), \(S = \begin{bmatrix} -1 & -5 \\ 1 & 6 \end{bmatrix}\)
\(w_1 = \begin{bmatrix} \\ \\ \end{bmatrix}\)
\(w_2 = \begin{bmatrix} \\ \\ \end{bmatrix}\)