Suppose \(A\) is a non-singular \(3\times 3\) matrix. Let \(A^{-1}=\begin{bmatrix}|&|&|\\\vec {d}_1& \vec {d}_2 & \vec {d}_3\\|&|&|\end{bmatrix}\).

Suppose \(A\begin{bmatrix}2\\3\\4\end{bmatrix}=\begin{bmatrix}5\\6\\7\end{bmatrix}\)

Express \(\begin{bmatrix}2\\3\\4\end{bmatrix}\) as a linear combination of the columns of \(A^{-1}\).

\[\begin{bmatrix}2\\3\\4\end{bmatrix}=\answer {5}\vec {d}_1+\answer {6}\vec {d}_2+\answer {7}\vec {d}_3\]