3.
$$\mathbf { M } = \left( \begin{array} { c c c }
3 & - 4 & k
1 & - 2 & k
1 & - 5 & 5
\end{array} \right) \text { where } k \text { is a constant }$$
Given that 3 is an eigenvalue of \(\mathbf { M }\),
- find the value of \(k\).
- Hence find the other two eigenvalues of \(\mathbf { M }\).
- Find a normalised eigenvector corresponding to the eigenvalue 3
.
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