91Ó°ÊÓ

Given a square matrix \(A^{-1}\), find matrix \(A\). $$A^{-1}=\left[\begin{array}{rrr} \frac{2}{3} & -\frac{1}{3} & 0 \\ \frac{1}{3} & -\frac{5}{3} & 1 \\ \frac{1}{3} & \frac{1}{3} & 0 \end{array}\right]$$

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

Use Cramer's rule to solve each system of equations. If \(D=0,\) use another method to complete the solution. $$\begin{array}{r}2 x-3 y=-5 \\\x+5 y=17\end{array}$$

Given a square matrix \(A^{-1}\), find matrix \(A\). $$A^{-1}=\left[\begin{array}{lll} 0 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array}\right]$$

Concept Check Fill in each blank with the appropriate response. The graph of the system $$ y > x^{2}+2 $$ $$ \begin{array}{r} x^{2}+y^{2}<16 \\ y<7 \end{array} $$ consists of all points \(\frac{\text { the parabola given by }}{\text { (above/below) }}\) \(y=x^{2}+2, \frac{ }{\text { (inside/outside) }}\) the circle \(x^{2}+y^{2}=16,\) and (above/below) the line \(y =7\)

Solve each system. Write solutions in terms of \(z\) if necessary. $$\begin{aligned} 3 x+6 y-3 z &=12 \\ -x-2 y+z &=16 \\ x+y-2 z &=20 \end{aligned}$$

Use Cramer's rule to solve each system of equations. If \(D=0,\) use another method to complete the solution. $$\begin{array}{l}x+9 y=-15 \\\3 x+2 y=5\end{array}$$

The values in the table are from a quadratic function \(f(x)=a x^{2}+b x+c .\) Find \(a, b,\) and \(c\). $$\begin{array}{c|c|c|c|c|c}x & -2 & -1 & 0 & 1 & 2 \\\\\hline f(x) & 2.9 & 1.26 & 0.56 & 0.8 & 1.98 \end{array}$$

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

Solve each system graphically. Check your solutions. Do not use a calculator. $$\begin{aligned}&x-y^{2}=1\\\&x^{2}+y^{2}=5\end{aligned}$$