GATE ECE 2015 Set 1 | Question: 5

Question

The value of $p$ such that the vector $\begin{bmatrix} 1 \\ 2 \\ 3 \end{bmatrix}$ is an eigenvector of the matrix $\begin{bmatrix} 4 & 1 & 2 \\ p & 2 & 1 \\ 14 & -4 & 10 \end{bmatrix}$ is _________.

Answer 1

Av=xv where v is an eigen vector and x is an eigen value. 

Substituting the matrix and vector and performing multiplication gives (12,7+p,36),

Our vector is (1,2,3) equating both gives 12(1,2,3) so 7+p=24 

P=24-7

P=17