Moderate -0.5 This is a triangular matrix where eigenvalues can be read directly from the diagonal (1, 2, -3), and finding eigenvectors requires solving three straightforward systems (A - λI)v = 0. While it involves matrix algebra and multiple calculations, it's a standard textbook exercise with no conceptual difficulty or problem-solving required.
1 It is given that
$$\mathbf { A } = \left( \begin{array} { r r r }
1 & - 1 & - 2 \\
0 & 2 & 1 \\
0 & 0 & - 3
\end{array} \right)$$
Write down the eigenvalues of \(\mathbf { A }\) and find corresponding eigenvectors.
1 It is given that
$$\mathbf { A } = \left( \begin{array} { r r r }
1 & - 1 & - 2 \\
0 & 2 & 1 \\
0 & 0 & - 3
\end{array} \right)$$
Write down the eigenvalues of $\mathbf { A }$ and find corresponding eigenvectors.
\hfill \mbox{\textit{CAIE FP1 2006 Q1 [5]}}