91Ó°ÊÓ

Find the eigenvalues and eigenvectors of the following matrices.\(\left(\begin{array}{ll}1 & 3 \\ 2 & 2\end{array}\right)\)

Find the eigenvalues and eigenvectors of the following matrices.\(\left(\begin{array}{rr}3 & -2 \\ -2 & 0\end{array}\right)\)

Find the eigenvalues and eigenvectors of the following matrices.\(\left(\begin{array}{rrr}2 & 0 & 2 \\ 0 & 2 & 0 \\ 2 & 0 & -1\end{array}\right)\)

Find the eigenvalues and eigenvectors of the following matrices.\(\left(\begin{array}{rrr}-1 & 1 & 3 \\ 1 & 2 & 0 \\ 3 & 0 & 2\end{array}\right)\)

Find the eigenvalues and eigenvectors of the following matrices.\(\left(\begin{array}{lll}1 & 2 & 2 \\ 2 & 3 & 0 \\ 2 & 0 & 3\end{array}\right)\)

Find the eigenvalues and eigenvectors of the following matrices.\(\left(\begin{array}{rrr}1 & 1 & 1 \\ 1 & -1 & 1 \\ 1 & 1 & -1\end{array}\right)\)

Find the eigenvalues and eigenvectors of the following matrices.\(\left(\begin{array}{rrr}-3 & 2 & 2 \\ 2 & 1 & 3 \\ 2 & 3 & 1\end{array}\right)\)

Find the eigenvalues and eigenvectors of the following matrices.\(\left(\begin{array}{rrr}13 & 4 & -2 \\ 4 & 13 & -2 \\ -2 & -2 & 10\end{array}\right)\)

Find the eigenvalues and eigenvectors of the following matrices.\(\left(\begin{array}{lll}3 & 2 & 4 \\ 2 & 0 & 2 \\ 4 & 2 & 3\end{array}\right)\)

Given \(\mathbf{V}=2 \mathbf{i}-3 \mathrm{j}, \mathbf{U}=\mathbf{i}+2 \mathbf{k}\), write the dyadics \(\mathbf{U} \mathbf{V}\) and \(\mathbf{V U}\) in dyadic and in matrix form. Find \(\mathbf{W}=(\mathrm{UV}) \cdot \mathbf{U}\) and write this equation in matrix form.