Question

[1, 1, 2] is an eigen vector of the matrix, $A=\left[\begin{array}{ccc}3& 1& -1\\ 2& 2& -1\\ 2& 2& 0\end{array}\right]$ corresponding to the eigen value x. The value of x is _______ .

• A. 2

Answer 1

The correct option is A 2
We know that,

$AX=\left[\begin{array}{ccc}3& 1& -1\\ 2& 2& -1\\ 2& 2& 0\end{array}\right]\left[\begin{array}{c}1\\ 1\\ 2\end{array}\right]=\left[\begin{array}{c}3+1-2\\ 2+2-2\\ 2+2+0\end{array}\right]=\left[\begin{array}{c}2\\ 2\\ 4\end{array}\right]=2\left[\begin{array}{c}1\\ 1\\ 2\end{array}\right]$

Comparing with $AX=\lambda X$

$\therefore$ $\lambda =2$

Hence, Eigen value $x=2$