Question

The value of P such that the vectoe $\left[\begin{array}{c}1\\ 2\\ 3\end{array}\right]$ is an eigen vector of the matrix $\left[\begin{array}{ccc}4& 1& 2\\ p& 2& 1\\ 14& -4& 10\end{array}\right]$ is

Answer 1

AX = $\lambda$X

$\left[\begin{array}{ccc}4& 1& 2\\ p& 2& 1\\ 14& -4& 10\end{array}\right]\left[\begin{array}{c}1\\ 2\\ 3\end{array}\right]=\lambda \left[\begin{array}{c}1\\ 2\\ 3\end{array}\right]$

$\Rightarrow$ $\lambda$ = 12 & 2$\lambda$ = p + 7

$\Rightarrow$ p = 17