3. \(\mathbf { M } = \left( \begin{array} { r r r } 3 & k & 2
- 1 & 0 & 1
1 & k & 1 \end{array} \right)\), where \(k\) is a constant
Given that 3 is an eigenvalue of \(\mathbf { M }\),
- find the value of \(k\).
- Hence find the other two eigenvalues of \(\mathbf { M }\).
- Find an eigenvector corresponding to the eigenvalue 3
3. \(\quad \mathbf { M } = \left( \begin{array} { r c c } 3 & k & 2
- 1 & 0 & 1
1 & k & 1 \end{array} \right)\), where \(k\) is a constant Given that 3 is an eigenvalue of \(\mathbf { M }\), (a) find the value of \(k\).