91Ó°ÊÓ

Solve each system graphically. Check your solutions. Do not use a calculator. $$\begin{aligned}&x-y=3\\\&x^{2}+y^{2}=9\end{aligned}$$

Find each matrix product if possible. $$\left[\begin{array}{rrr}-1 & 2 & 0 \\ 0 & 3 & 2 \\ 0 & 1 & 4\end{array}\right]\left[\begin{array}{rrr}2 & -1 & 2 \\ 0 & 2 & 1 \\ 3 & 0 & -1\end{array}\right]$$

Graph the solution set of each system of inequalities by hand. $$\begin{array}{l}-2

Solve each system graphically. Check your solutions. Do not use a calculator. $$\begin{aligned}&x^{2}-y=0\\\&x^{2}+y^{2}=2\end{aligned}$$

Graph the solution set of each system of inequalities by hand. $$\begin{array}{r}-21 \\\x-y>0\end{array}$$

Solve each system. Write solutions in terms of \(z\) if necessary. $$\begin{array}{r} x-3 y+2 z=10 \\ 2 x-y-z=15 \end{array}$$

Use Cramer's rule to solve each system of equations. If \(D=0,\) use another method to complete the solution. $$\begin{aligned}&4 x-y+3 z=-3\\\&3 x+y+z=0\\\&2 x-y+4 z=0\end{aligned}$$

Find each matrix product if possible. $$\left[\begin{array}{lll}-2 & 4 & 1\end{array}\right]\left[\begin{array}{rrr}3 & -2 & 4 \\ 2 & 1 & 0 \\ 0 & -1 & 4\end{array}\right]$$

Let \(A=\left[\begin{array}{lll}a & 0 & 0 \\ 0 & b & 0 \\ 0 & 0 & c\end{array}\right],\) where \(a, b,\) and \(c\) are nonzero real numbers. Find \(A^{-1}\).

Graph the solution set of each system of inequalities by hand. $$\begin{aligned}&x+y \leq 4\\\&\begin{array}{c}x-y \leq 5 \\\4 x+y \leq-4\end{array}\end{aligned}$$