Math Problem Solver

The eigenvalues of the matrix are: $$\begin{aligned} \lambda_{1} &= -2\\ \lambda_{2} &= 4 \end{aligned}$$ $\lambda_{1}$ has multiplicity 2. All other eigenvalues have multiplicity 1.
The eigenvectors $\begin{bmatrix}1\\1\\0\end{bmatrix}$ , $\begin{bmatrix}-1\\0\\1\end{bmatrix}$ are associated with the eigenvalue $\lambda_{1}$.
The eigenvector $\begin{bmatrix}\frac{1}{2}\\\frac{1}{2}\\1\end{bmatrix}=\begin{bmatrix}0.5\\0.5\\1\end{bmatrix}$ is associated with the eigenvalue $\lambda_{2}$.