1.11.9 Tensor calculus

Problem: Given the covariant metric tensor \( \left(g_{i j}\right)=\left(\begin{array}{ll}2 & 3 \\ 3 & 5\end{array}\right) \) and tensor \( \left(a_{\cdot j k}^{i}\right)=\left(\begin{array}{ll|ll}3 & 4 & 2 & 5 \\ 5 & 7 & 1 & 3\end{array}\right) \). Find matrices of the tensors: 1) \( a_{i j k} \), 2) \( a_{\cdot \cdot k}^{i j} \), 3) \( a_{. j .}^{i \cdot k} \), 4) \( a^{i j k} \).