1.4.45 Matrix transformations

condition: Find the matrix of the linear operator \( A \) in the canonical basis and in the basis \( \left\{a_{1}, a_{2}\right\} \), if \( A a_{i}=b_{i},(i=1,2) \), where \( a_{1}=\left(\begin{array}{l}1 \\ 4\end{array}\right), a_{2}=\left(\begin{array}{c}-2 \\ 1\end{array}\right) \), \( b_{1}=\left(\begin{array}{l}1 \\ 1\end{array}\right), b_{2}=\left(\begin{array}{l}-1 \\ -2\end{array}\right) \).