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