2.
$$\mathbf { M } = \left( \begin{array} { l l l }
1 & 0 & 2
0 & 4 & 1
0 & 5 & 0
\end{array} \right)$$
- Show that matrix \(\mathbf { M }\) is not orthogonal.
- Using algebra, show that 1 is an eigenvalue of \(\mathbf { M }\) and find the other two eigenvalues of \(\mathbf { M }\).
- Find an eigenvector of \(\mathbf { M }\) which corresponds to the eigenvalue 1
The transformation \(M : \mathbb { R } ^ { 3 } \rightarrow \mathbb { R } ^ { 3 }\) is represented by the matrix \(\mathbf { M }\).
- Find a cartesian equation of the image, under this transformation, of the line
$$x = \frac { y } { 2 } = \frac { z } { - 1 }$$