Find the eigenvalues and eigenvectors of the matrix:
\[\begin{bmatrix} -1 & 0 \\ -4 & -5 \end{bmatrix}\]Click for answer
Your answer may differ by scaling eigenvectors (columns of \(P\)) or otherwise choosing a different basis for the eigenspace.
Click for Latex code
\[ \begin{bmatrix} -1 & 0 \\ -4 & -5 \end{bmatrix} \]Diagonalization:
\begin{solution} \[ \begin{bmatrix} -1 & 0 \\ -4 & -5 \end{bmatrix} = \begin{bmatrix} -1 & 0 \\ 1 & -1 \end{bmatrix} \begin{bmatrix} -1 & 0 \\ 0 & -5 \end{bmatrix} \begin{bmatrix} -1.0 & -0.0 \\ -1.0 & -1.0 \end{bmatrix} \] \end{solution}