Solve each system by the substitution method . Be sure to check all proposed solutions.

$$\left\{ \begin{array} { r } { x + 8 y = 6 } \\ { 2 x + 4 y = - 3 } \end{array} \right.$$

Use a graphing calculator to find the inverse of the matrix, if it exists.

$$\left[\begin{array}{lll}{1} & {7} & {3} \\ {0} & {2} & {1} \\ {0} & {0} & {3}\end{array}\right]$$

Graph each piecewise-defined function. See the examples in this chapter.

$$f(x)=\left\{\begin{array}{rll}4 & \text { if } & x<-3 \\ -2 & \text { if } & x \geq-3\end{array}\right.$$

Let

$$A=\left[\begin{array}{ll}4 & 2 \\ 1 & 3\end{array}\right]$$

. Find (a) $A^2+3 A$ (b) $2 A^3+3 A^2+4 A+5 I_2$

In each exercise, $\lambda$ is an eigenvalue of the given matrix $A$. Determine an eigenvector corresponding to $\lambda$.

$$A=\left[\begin{array}{rr}5 & 3 \\ -4 & -3\end{array}\right], \lambda=-1$$

Solve the system.

$$\left\{\begin{array}{l} \frac{3}{x-1}+\frac{4}{y+2}=2 \\ \frac{6}{x-1}-\frac{7}{y+2}=-3 \end{array}\right.$$

Find inverse of matrix $A$ i.e. $A^{-1}$, if possible. Where $A$ is given by :

$$A=\begin{bmatrix} \frac{1}{4} & 2 \\[3pt] \frac{1}{3} & \frac{2}{3} \end{bmatrix}$$

What is the value of

$$log_4 \frac { 1 } { 64 } ?$$

$$\left. \begin{array} { l } { A - 3 } \\ { B - \frac { 1 } { 3 } } \\ { C \frac { 1 } { 3 } } \\ { D 3 } \end{array} \right.$$

Let A

$$A = \left[ \begin{array} { c c c } { 4 } & { - 1 } & { - 4 } \\ { 3 } & { 0 } & { - 4 } \\ { 3 } & { - 1 } & { - 3 } \end{array} \right]$$

Show that $A ^ { 2 } = I$

Use Cramer's rule, if possible, to solve each system of linear equations.

$$\left\{\begin{array}{l}3 x+6 y=15 \\ 2 x+4 y=3\end{array}\right.$$

Perform the indicated multiplications.

$$\begin{bmatrix} -1 & 7 \\ 3 & 5 \\ 10 & -1 \\ -5 & 12 \end{bmatrix} \begin{bmatrix} 2 & 1 \\ 5 & -3 \end{bmatrix}$$

Solve by graphing and then find an exact solution by using either substitution or elimination:

$$\left\{\begin{array}{l} 2 x-3 y=-9 \\ 2 x+3 y=-3 \end{array}\right.$$

Solve the system of linear equations.

$$\left\{\begin{aligned} x-3 y+2 z+w &=-2 \\ x-2 y \quad -2 w &=-10 \\ z+5 w &=15 \\ 3 x\quad+2 z+w &=-3 \end{aligned}\right.$$

Circle the letter which word carries a similar meaning to the requested example word.

quandary = a state of (a) doubt, (b) certainty, (c) depression, (d) apprehension