LINEAR ALGEBRA (Math 211)
HW #8 (Due Mon. Oct. 23 )

For the following matrices find the characteristic equation, eigenvalues, and the corresponding eigenvectors

1. $\left(\begin{array}{rr} 1&2\\ 2&1 \end{array}\right)$                 2. $\left(\begin{array}{rr} 2&3\\ 4&3 \end{array}\right)$                 3. $\left(\begin{array}{rr} 3&1\\ -5&3 \end{array}\right)$                 4. $\left(\begin{array}{rrr} 1&2&1\\ 0&3&1\\ -1&1&0\\ \end{array}\right)$


Compute the following determinants


5. $\left\vert\begin{array}{rrrr} 2&0&0&0\\ 0&0&3&0\\ 0&-1&0&0\\ 0&0&0&4 \end{array}\right\vert$                 6. $\left\vert\begin{array}{rrrr} 1&1&-1&0\\ -3&4&6&0\\ 2&5&-1&3\\ 4&0&3&0 \end{array}\right\vert$