Eigenvalues and Eigenvectors
\(A = \begin{bmatrix} 1 & 1 & 0 \\ 1 & 0 & 1 \\ 0 & 1 & 1 \end{bmatrix}\)
\(v = \begin{bmatrix} a \\ b \\ c \end{bmatrix}\)
\(Av = \lambda v \qquad \)\(a, b, c, v \in \mathbb{C}\)
\(\Rightarrow Av - \lambda v = 0\)
\(\Rightarrow (A - \lambda I_3) v = 0\)