3 Find a matrix \(\mathbf { A }\) whose eigenvalues are \(- 1,1,2\) and for which corresponding eigenvectors are
$$\left( \begin{array} { l }
1 \\
0 \\
0
\end{array} \right) , \quad \left( \begin{array} { l }
1 \\
1 \\
0
\end{array} \right) , \quad \left( \begin{array} { l }
0 \\
1 \\
1
\end{array} \right) ,$$
respectively.
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3 Find a matrix $\mathbf { A }$ whose eigenvalues are $- 1,1,2$ and for which corresponding eigenvectors are
$$\left( \begin{array} { l }
1 \\
0 \\
0
\end{array} \right) , \quad \left( \begin{array} { l }
1 \\
1 \\
0
\end{array} \right) , \quad \left( \begin{array} { l }
0 \\
1 \\
1
\end{array} \right) ,$$
respectively.
\hfill \mbox{\textit{CAIE FP1 2016 Q3}}