3.
You are given the matrix \(\mathbf { A } = \left( \begin{array} { c c c } 1 & 0 & 0
0 & 0 & 1
0 & - 1 & 0 \end{array} \right)\).
- Find \(\mathbf { A } ^ { 4 }\).
- Describe the transformation that \(\mathbf { A }\) represents.
The matrix \(\mathbf { B }\) represents a reflection in the plane \(x = 0\).
- Write down the matrix B.
The point \(P\) has coordinates \(( 2,3,4 )\). The point \(P ^ { \prime }\) is the image of \(P\) under the transformation represented by \(\mathbf { B }\).
- Find the coordinates of \(P ^ { \prime }\).
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