Fid bet basb le s a for which the system of equations
$$\begin{array} { r l }
x - 2 y - 2 z + z & 0
2 x + ( a - 9 y - 0 z + 1 E & 0
3 x - 6 y + 2 a z + 9 & 0
\end{array}$$
h san q sbtu in
Given that \(a = - 3\), show that the system of equations in part (i) \(\mathbf { b } \mathbf { s } \mathbf { n }\) sb t in In erp et th s situation geometrically.
The matrix \(\mathbf { A }\) is given by
$$\mathbf { A } = \left( \begin{array} { r r r }
1 & 1 & 2
0 & 2 & 2
- 1 & 1 & 3
\end{array} \right)$$
Find b eig le so A.
Use th ch racteristic eq tiw \(\mathbf { A }\) tof id \(\mathbf { A } ^ { - 1 }\).
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