PROBLEM $(19)$: $,A_{\text{i}\text{j}\text{k}}$ is a third $-$ order tensor, such that $A_{111}=A_{222}=1,A_{212}=-2,$ all

other components being zero. Evaluate the components of the vector $A_{\text{i}\text{j}\text{i}}.$

The same transformation is made from $O{x}_1{x}_2{x}_3$ to $O{x}_1^{\text{'}}{x}_2^{\text{'}}{x}_3^{\text{'}}$ as in problem

$(18).$ Evaluate the component $A_{123}^{\text{'}}$ of the tensor in the system $O{x}_1^{\text{'}}{x}_2^{\text{'}}{x}_3^{\text{'}}.$