LINEAR ALGEBRA (Math 211)
HW #9 (Due Wed. Oct. 25 )

Compute the following determinants


1. $\left\vert\begin{array}{rrrr} 1&2&0&0\\ 3&-2&3&0\\ 0&0&1&-5\\ 0&0&7&2 \end{array}\right\vert$                 2. $\left\vert\begin{array}{rrrr} a&b&0&0\\ c&d&0&0\\ 0&0&e&f\\ 0&0&g&h \end{array}\right\vert$

3. Using the determinant calculate an inverse matrix A-1 for $A=\left(\begin{array}{rrr} 2&4&3\\ 0&1&-1\\ 3&5&7 \end{array}\right)$ .


Solve the following systems by using Cramer's rule


4.     $\left\{\begin{array}{rrrrr} x_1&-x_2&+x_3&=&7\\ 2x_1&&-5x_3&=&4\\ &3x_2&-x_3&=&2 \end{array}\right.$                 5.     $\left\{\begin{array}{rrrrr} 2x_1&+3x_2&-x_3&=&5\\ -x_1&+2x_2&+3x_3&=&0\\ 4x_1&-x_2&+x_3&=&-1 \end{array}\right.$