(Solved):   3- For the matrix representation of tensor \( \boldsymbol{T} \) shown below, \[ \left[t_{i ...

 

3- For the matrix representation of tensor \( \boldsymbol{T} \) shown below, \[ \left[t_{i j}\right]=\left[\begin{array}{ccc} 5 & 1 & \sqrt{2} \\ 1 & 5 & \sqrt{2} \\ \sqrt{2} & \sqrt{2} & 6 \end{array}\right] \] (a) If \( \lambda_{1}=8 \), determine the two other eigenvalues of \( \left[t_{i j}\right] \) (b) The eigenvectors of \( \left[t_{i j}\right] \) associated with the eigenvalues in (a).