1.11.5 Tensor calculus

Problem: Tensor type (1,2) in the basis \( \mathcal{E}=\left\{e_{1}, e_{2}\right\} \) of the space \( V_{2} \) is given by the matrix \( A= \) \( \left(\begin{array}{ll|ll}-4 & 2 & 3 & 4 \\ -5 & 3 & 5 & 7\end{array}\right) \), where \[ \left\{\begin{array}{l} e_{1}^{\prime}=e_{1}-e_{2} \\ e_{2}^{\prime}=-e_{1}+2 e_{2} \end{array} .\right. \] Find tensor matrix in basis \( \mathcal{E}^{\prime}=\left\{e_{1}^{\prime}, e_{2}^{\prime}\right\} \).