Draw the directed graph that represents the data in the communications matrix.

$$\begin{array}{r} A \\ B \\ C \end{array} \normalsize \overset{A\quad B\quad C } {\left[\begin{array}{} 1 & 0 & 0 \\ 0 & 0 & 1 \\ 1 & 1 & 1 \end{array}\right]}\begin{array}{ll}\end{array}$$

Use the matrices given above to perform the indicated operations if they are defined. If an operation is not defined. label it "undefined."

$$C^2$$

Solve: $|3 x+8|>-6$

Use matrices $A, B, C, D, F$, and $G$ to perform the indicated operations. If an operation is not possible, explain why.

$$A-B$$

Determine the vector $\mathbf{v}$ with the given initial point $P$ and terminal point $Q$. Give both the component form and polar form.

$$P=(\sqrt{11},-\sqrt{2}), Q=(\sqrt{13}, \sqrt{3})$$

Solve the system:

$$\left\{\begin{array}{r}2 x+y=6 \\ x-2 y=8\end{array}\right.$$

Use the formula for the rotation matrix $R_{\mathrm{a}}$ to find an explicit expression for the given rotation matrix.

$$R_{270^{-}}$$

Determine whether the given pairs of vectors are parallel, perpendicular, or neither.

$$(13,8),\left(\frac{13}{4}, 2\right)$$

Solve each system of equations using the augmented matrix method.

$$\left\{\begin{array}{l}x+2 y-z=29 \\ 3 x-1.5 y+12 z=-18 \\ 2 x+0.5 y-5 z=39\end{array}\right.$$

Solve each matrix equation.

$$5 X-\left[\begin{array}{l}1 \\ 4\end{array}\right]=\left[\begin{array}{l}4 \\ 6\end{array}\right]$$

Show by multiplication that $B$ and $A$ are multiplicative inverses of each other.

$$\left[\begin{array}{rrr}5 & -3 & 2 \\ 2 & 4 & -3 \\ 4 & -2 & 5\end{array}\right]$$

In each item you are to compare a quantity in Column $1$ with a quantity in Column $2$. Write the letter of the correct answer from these choices: A. The quantity in Column $1$ is greater than the quantity in Column $2$. B. The quantity in Column $2$ is greater than the quantity in Column $1$. C. The quantity in Column $1$ is equal to the quantity in Column $2$. D. The relationship cannot be determined from the given information. Notes: Information centered over both columns refers to one or both of the quantities being compared. A symbol that appears in both columns has the same meaning in each column. All variables represent real numbers. Most figures are not drawn to scale.

$$\begin{array}{} \text{Column 1}&\text{Column 2}\\ \text{modulus of}\ 3-4 i& \text{modulus of} 6+3 i \end{array}$$

Determine whether the given pairs of vectors are parallel, perpendicular, or neither.

$$(-12,9),(4,-3)$$

Find the measure of the angle between the given vectors.

$$(3,4),(-4,3)$$