2.
$$\mathbf { P } = \frac { 1 } { 2 } \left( \begin{array} { r r }
1 & \sqrt { 3 }
- \sqrt { 3 } & 1
\end{array} \right) \quad \mathbf { Q } = \left( \begin{array} { r r }
- 1 & 0
0 & 1
\end{array} \right)$$
The matrices \(\mathbf { P }\) and \(\mathbf { Q }\) represent linear transformations, \(P\) and \(Q\) respectively, of the plane.
The linear transformation \(M\) is formed by first applying \(P\) and then applying \(Q\).
- Find the matrix \(\mathbf { M }\) that represents the linear transformation \(M\).
- Show that the invariant points of the linear transformation \(M\) form a line in the plane, stating the equation of this line.
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