Exam 9: Systems and Matrices

Solve the problem. -Caroleʹs car averages 12.9 mi/gal in city driving and 21.8 mi/gal in highway driving. If she drove a total of 320.3 mi on 20 gal of gas, how many of the gallons were used for city driving?

Solve the system. If the system has infinitely many solutions, write the solution set with x arbitrary. - $7 x - y = 5$ $- 14 x + 2 y = - 10$

Use the Gauss-Jordan method to solve the system of equations. If the system has infinitely many solutions, let the last variable be the arbitrary variable. - 2x-2y+3z=3 x+2y-z=7 2y+z=1

Which method should be used to solve the system? Explain your answer, including a description of the first step. - -3+10=4 x-5y=1

Write the system of equations associated with the augmented matrix. Do not solve. - $\left[ \begin{array} { l l | l } - 3 & 2 & - 2 \\ - 6 & 3 & - 9 \end{array} \right]$

Solve the system. If the system has infinitely many solutions, write the solution set with x arbitrary. - 8x+6y-z=-2 4x-y+2z=1 -16x-12y+2z=0

Graph the inequality. - $x+y<-4$

Find the indicated matrix. -Let $C = \left[ \begin{array} { r } 1 \\ - 3 \\ 2 \end{array} \right]$ and $D = \left[ \begin{array} { r } - 1 \\ 3 \\ 2 \end{array} \right]$ . Find $C - 2 D$ .

Use a graphing calculator and the method of matrix inverses to solve the system. Give five decimal places, if necessary. - $x - \sqrt { 2 } y = 3.7$ $2.85 x + y = - 8.23$

Graph the solution set of the system of inequalities. -

Write the augmented matrix for the system. Do not solve the system. - 5x+5y=15 7x+9y=17

Give all solutions of the nonlinear system of equations, including those with nonreal complex components. - xy=32 +=80

The sizes of two matrices are given. Find the size of the product AB and the size of the product BA, if the given product can be calculated. - $A$ is $2 \times 1$ ; B is $1 \times 1$ .

Find the values of the variables for which the statement is true, if possible. - $\left[ \begin{array} { l l } 7 & 7 \\x & 0\end{array} \right] = \left[ \begin{array} { c c } \mathrm { m } - 4 & \mathrm { n } + 4 \\2 & 0\end{array} \right]$

Write the augmented matrix for the system. Do not solve the system. - 3x+6y-2z=41 6x+5y+3z=26 2x+8y+7z=47

Determine the inequality which matches the calculator graph. Do not use your calculator. Instead, use your knowledge of the concepts involved in graphing inequalities. -

Solve the system. - 4x+2y+z=17 5x-3y-z=8 5x+y+5z=22

Solve the system. - x-y+5z=-14 2x+z=-2 x+5y+z=18

Find the matrix product when possible. - $\left[ \begin{array} { l l l } - 3 & 8 & - 2\end{array} \right] \left[ \begin{array} { r r r } 7 & 6 & - 2 \\- 1 & 2 & - 2 \\6 & - 7 & 6\end{array} \right]$

Give all solutions of the nonlinear system of equations, including those with nonreal complex components. - y=|x| 4x-y=-15