Question

If ${\left\{\begin{array}{ccc}1& 0& -1\end{array}\right\}}^T$ is an eigen vector of the following matrix $\left[\begin{array}{ccc}1& -1& 0\\ -1& 2& -1\\ 0& -1& 1\end{array}\right]$ then the corresponding eigen value is

• A. 1
• B. 2
• C. 3
• D. 5

Answer 1

The correct option is A 1

$AX=\lambda X$
$\left[\begin{array}{ccc}1& -1& 0\\ -1& 2& -1\\ 0& -1& 1\end{array}\right]\left[\begin{array}{c}1\\ 0\\ -1\end{array}\right]=\lambda \left[\begin{array}{c}1\\ 0\\ -1\end{array}\right]$
$\left[\begin{array}{c}1\\ 0\\ -1\end{array}\right]=\lambda \left[\begin{array}{c}1\\ 0\\ -1\end{array}\right]$
$\Rightarrow \lambda =1$