[Steps Shown] Define P, X, O and I as follows:
Question: Define \(\mathbf{P}, \mathbf{X}, \mathbf{O}\) and \(\mathbf{I}\) as follows:
\[\mathbf{P}=\left(\begin{array}{ccc} 0 & 0 & 0 \\ 0 & 1 & 1 \\ 0 & 1 & 1 \end{array}\right) \quad \mathbf{X}=\left(\begin{array}{l} x \\ y \\ z \end{array}\right) \quad \mathbf{O}=\left(\begin{array}{l} 0 \\ 0 \\ 0 \end{array}\right) \quad \mathbf{I}=\left(\begin{array}{ccc} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{array}\right)\]Solve each of the following equations:
\[\mathbf{P X}=\mathbf{O} \quad(\mathbf{P}-2 \mathbf{I}) \mathbf{X}=\mathbf{O}\]
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