Eigenvalues

Eigenvalues and Eigenvectors

$A = \begin{bmatrix} 1 & 1 & 0 \\ 1 & 0 & 1 \\ 0 & 1 & 1 \end{bmatrix}$

$v = \begin{bmatrix} a \\ b \\ c \end{bmatrix}$

$Av = \lambda v \qquad $$a, b, c, v \in \mathbb{C}$

$\Rightarrow Av - \lambda v = 0$

$\Rightarrow (A - \lambda I_3) v = 0$