Find the inverse, if it exists, for the matrix.

$$\left[\begin{array}{rrr}1 & 0 & 0 \\ 0 & -1 & 0 \\ 1 & 0 & 1\end{array}\right]$$

Find the size of the matrix. Identify any square, col

$$\left[\begin{array}{l}2 \\ 4\end{array}\right]$$

This exercise has introduced methods for solving systems of equations, including substitution and elimination, and matrix methods such as the Gauss-Jordan method and Cramer's rule. Use each method at least once when solving the systems. Include solutions with nonreal complex number components. For systems with infinitely many solutions, write the solution set using an arbitrary variable.

$$\begin{aligned} & -5 x+2 y+z=5 \\ & -3 x-2 y-z=3 \\ & -x+6 y=1 \end{aligned}$$

Write a system of linear equations, and then use the system to solve the problem.

The Waputi Indians make woven blankets, rugs, and skirts. Each blanket requires $24 \mathrm{hr}$ for spinning the yarn, $4 \mathrm{hr}$ for dyeing the yarn, and $15 \mathrm{hr}$ for weaving. Rugs require $30$,$5$ , and $18 \mathrm{hr}$ and skirts $12$,$3$ , and $9 \mathrm{hr}$, respectively. If there are $306$,$59$ , and $201 \mathrm{hr}$ available for spinning, dyeing, and weaving, respectively, how many of each item can be made?

(Hint: Simplify the equations you write, if possible, before solving the system.)

Find the value of the determinant.

$$\left|\begin{array}{rrr}1 & 2 & 0 \\ -1 & 2 & -1 \\ 0 & 1 & 4\end{array}\right|$$

Solve the nonlinear system of equations.

$$\begin{aligned} & x^2+y^2=25 \\ & x+y=7 \end{aligned}$$

Find the inverse, if it exists, for the matrix.

$$\left[\begin{array}{rrr}1 & 0 & 1 \\ 0 & -1 & 0 \\ 2 & 1 & 1\end{array}\right]$$

Find the partial fraction decomposition for the rational expression.

$$\frac{x^3+4}{9 x^3-4 x}$$

Solve the given system by substitution.

$$\begin{aligned} &3 y=5 x+6 \\ &x+y=2 \end{aligned}$$

Graph the inequality.

In your own words, explain how to determine whether the boundary of the graph of an inequality is solid or dashed.

Graph the inequality.

$$(x-4)^2+(y+3)^2 \leq 9$$

Write a system of linear equations, and then use the system to solve the problem.

A company sells recordable CDs for $80 \%$ each and play-only CDs for $60 \%$ each. The company receives $\$ 76$ for an order of $100$ CDs. However, the customer neglected to specify how many of each type to send. Determine the number of each type of CD that should be sent.

Solve the given system by substitution.

$$\begin{aligned} &3 x-7 y=15 \\ &3 x+7 y=15 \end{aligned}$$

Give all solutions of the nonlinear system of equations, including those with nonreal complex components.

$$\begin{array}{r} x^2+y^2=5 \\ -3 x+4 y=2 \end{array}$$