Question 1

Solve the system.
-$$\begin{array} { l } 
\frac { 1 } { x } + \frac { 1 } { y } + \frac { 1 } { z } = \frac { 19 } { 20 } \
\frac { 1 } { x } - \frac { 1 } { y } - \frac { 7 } { z } = - \frac { 69 } { 20 } \
\frac { 9 } { x } + \frac { 1 } { y } + \frac { 1 } { z } = \frac { 59 } { 20 }
\end{array}$$

Accepted Answer

A)  $\{ ( 4,5 , - 2 ) \}$ 
B)  $\{ ( 4,5,2 ) \}$ 
C)  $\left\{ \left( \frac { 1 } { 4 } , \frac { 1 } { 5 } , \frac { 1 } { 2 } \right) \right\}$ 
D)  $\{ ( - 4 , - 5,2 ) \}$ 
A)  $\{ ( 4,5 , - 2 ) \}$ 
B)  $\{ ( 4,5,2 ) \}$ 
C)  $\left\{ \left( \frac { 1 } { 4 } , \frac { 1 } { 5 } , \frac { 1 } { 2 } \right) \right\}$ 
D)  $\{ ( - 4 , - 5,2 ) \}$

Question 2

Find the partial fraction decomposition for the rational expression.
-$\frac { 4 x ^ { 3 } + 8 x ^ { 2 } - 6 x + 2 } { 2 x ^ { 2 } - x - 1 }$

Accepted Answer

A)  $2 x - 5 + \frac { - 13 } { 2 x + 1 } + \frac { 7 } { x - 1 }$ 
B)  $2 x + 5 + \frac { - 7 } { 6 x + 3 } + \frac { 13 } { 3 x - 3 }$ 
C)  $2 x - 5 + \frac { - 5 } { 6 x + 3 } + \frac { 1 } { 3 x - 3 }$ 
D)  $2 x + 5 + \frac { - 13 } { 6 x + 3 } + \frac { 8 } { 3 x - 3 }$ 
A)  $2 x - 5 + \frac { - 13 } { 2 x + 1 } + \frac { 7 } { x - 1 }$ 
B)  $2 x + 5 + \frac { - 7 } { 6 x + 3 } + \frac { 13 } { 3 x - 3 }$ 
C)  $2 x - 5 + \frac { - 5 } { 6 x + 3 } + \frac { 1 } { 3 x - 3 }$ 
D)  $2 x + 5 + \frac { - 13 } { 6 x + 3 } + \frac { 8 } { 3 x - 3 }$

Question 3

Provide an appropriate response.
-Fill in the blank to complete the statement. A matrix having the same number of rows as columns is called a? matrix.

Accepted Answer

A)  column 
B)  square 
C)  regular 
D)  rectangular 
A)  column 
B)  square 
C)  regular 
D)  rectangular

Question 4

Solve the problem.
-A company makes 3 types of cable. Cable A requires 3 black, 3 white, and 2 red wires. B requires 1 black, 2 white, and 1 red. C requires 2 black, 1 white, and 2 red. The company used 100 black, 110
White and 80 red wires. How many of each type of cable were made?

Accepted Answer

A)  20 A; 20 B; 83 C 
B) 20 A; 93 B; 10 C 
C) 10A; 20 B; 20 C 
D) 20 A; 20 B; 10 C 
A)  20 A; 20 B; 83 C 
B) 20 A; 93 B; 10 C 
C) 10A; 20 B; 20 C 
D) 20 A; 20 B; 10 C

Question 5

Give all solutions of the nonlinear system of equations, including those with nonreal complex components.
-$$\begin{array} { l } 
2 x ^ { 2 } - 3 y ^ { 2 } = 38 \
3 x ^ { 2 } + 5 y ^ { 2 } = 95
\end{array}$$

Accepted Answer

A)  $\{ ( 5,2 ) , ( 2,5 ) , ( - 5 , - 2 ) , ( - 2 , - 5 ) \}$ 
B)  $\{ ( 5 , - 2 ) , ( 5,2 ) \}$ 
C)  $\{ ( - 5 , - 2 ) , ( - 2 , - 5 ) \}$ 
D)  $\{ ( 5,2 ) , ( - 5,2 ) , ( 5 , - 2 ) , ( - 5 , - 2 ) \}$ 
A)  $\{ ( 5,2 ) , ( 2,5 ) , ( - 5 , - 2 ) , ( - 2 , - 5 ) \}$ 
B)  $\{ ( 5 , - 2 ) , ( 5,2 ) \}$ 
C)  $\{ ( - 5 , - 2 ) , ( - 2 , - 5 ) \}$ 
D)  $\{ ( 5,2 ) , ( - 5,2 ) , ( 5 , - 2 ) , ( - 5 , - 2 ) \}$

Question 6

Write the augmented matrix for the system. Do not solve the system.
-$$\begin{array} { l } 
9 x + 3 y = 78 \
7 x + 5 y = 58
\end{array}$$

Accepted Answer

A) 
$\left[\begin{array}{ll|l}
9 & 7 & 78 \
3 & 5 & 58
\end{array}\right]$ 
B) 
$\left[\begin{array}{ll|l}
78 & 3 & 9 \
58 & 7 & 5
\end{array}\right]$ 
C) 
$\left[\begin{array}{ll|l}
9 & 3 & 58 \
5 & 7 & 78
\end{array}\right]$ 
D) 
$\left[\begin{array}{ll|l}
9 & 3 & 78 \
7 & 5 & 58
\end{array}\right]$ 
A) 
$\left[\begin{array}{ll|l}
9 & 7 & 78 \
3 & 5 & 58
\end{array}\right]$ 
B) 
$\left[\begin{array}{ll|l}
78 & 3 & 9 \
58 & 7 & 5
\end{array}\right]$ 
C) 
$\left[\begin{array}{ll|l}
9 & 3 & 58 \
5 & 7 & 78
\end{array}\right]$ 
D) 
$\left[\begin{array}{ll|l}
9 & 3 & 78 \
7 & 5 & 58
\end{array}\right]$

Question 7

Provide an appropriate response.
-Suppose that you are solving a system of three linear equations by the Gauss-Jordan method and obtain the following augmented matrix.
$$\left[ \begin{array} { r r r | r } 
1 & 7 & 18 & 24 \
0 & 0 & 0 & 0 \
0 & 6 & 5 & - 25
\end{array} \right]$$
What conclusion can you draw about the solutions of the system?

Accepted Answer

A)  The system has infinitely many solutions. 
B)  The system has exactly one solution. 
C)  The system has no solutions. 
D)  There is not enough information to draw any conclusion about the solutions of the system. 
A)  The system has infinitely many solutions. 
B)  The system has exactly one solution. 
C)  The system has no solutions. 
D)  There is not enough information to draw any conclusion about the solutions of the system.

Question 8

Solve the equation for x.
-$\left| \begin{array} { l l } 2 & 4 \ \times & 3 \end{array} \right| = - 2$

Accepted Answer

A)  $\{ - 2 \}$ 
B)  $\{ - 1 \}$ 
C)  $\{ 2 \}$ 
D)  $\varnothing$ 
A)  $\{ - 2 \}$ 
B)  $\{ - 1 \}$ 
C)  $\{ 2 \}$ 
D)  $\varnothing$

Question 9

Solve the system.
-$$\begin{array} { c } 
x + y + z = - 4 \
x - y + 4 z = 21 \
2 x + y + z = - 8
\end{array}$$

Accepted Answer

A)  $\{ ( 5 , - 4 , - 5 ) \}$ 
B)  $\{ ( 5 , - 5 , - 4 ) \}$ 
C)  $\{ ( - 4 , - 5,5 ) \}$ 
D)  $\varnothing$ 
A)  $\{ ( 5 , - 4 , - 5 ) \}$ 
B)  $\{ ( 5 , - 5 , - 4 ) \}$ 
C)  $\{ ( - 4 , - 5,5 ) \}$ 
D)  $\varnothing$

Question 10

Use a graphing calculator to solve the system. Express solutions with approximations to the nearest thousandth.
-$\sqrt { 2 } x - y = 7$ $100 x + y = 9$

Accepted Answer

A)  $\{ ( 0.020,6.971 ) \}$ 
B)  $\{ ( 0.157 , - 6.686 ) \}$ 
C)  $\{ ( 0.154 , - 6.444 ) \}$ 
D)  $\{ ( 0.158 , - 6.777 ) \}$ 
A)  $\{ ( 0.020,6.971 ) \}$ 
B)  $\{ ( 0.157 , - 6.686 ) \}$ 
C)  $\{ ( 0.154 , - 6.444 ) \}$ 
D)  $\{ ( 0.158 , - 6.777 ) \}$

Question 11

Give all solutions of the nonlinear system of equations, including those with nonreal complex components.
-$x ^ { 2 } - y ^ { 2 } = 39$ $x - y = 3$

Accepted Answer

A)  $\{ ( 8,5 ) \}$ 
B)  $\{ ( - 8 , - 5 ) \}$ 
C)  $\{ ( 8 , - 5 ) \}$ 
D)  $\{ ( - 8,5 ) \}$ 
A)  $\{ ( 8,5 ) \}$ 
B)  $\{ ( - 8 , - 5 ) \}$ 
C)  $\{ ( 8 , - 5 ) \}$ 
D)  $\{ ( - 8,5 ) \}$

Question 12

Solve the system by elimination.
-$$\begin{array} { c } 
4 x + 7 y = 24 \
- 2 x + 2 y = - 12
\end{array}$$

Accepted Answer

A)  $\{ ( 6,0 ) \}$ 
B)  $\{ ( 6,1 ) \}$ 
C)  $\varnothing$ 
D)  $\{ ( 5,1 ) \}$ 
A)  $\{ ( 6,0 ) \}$ 
B)  $\{ ( 6,1 ) \}$ 
C)  $\varnothing$ 
D)  $\{ ( 5,1 ) \}$

Question 13

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

Accepted Answer

A)  $y \geq - 2$ 
B)  $x \geq - 2$ 
C)  $x \leq - 2$ 
D)  $y \leq - 2$ 
A)  $y \geq - 2$ 
B)  $x \geq - 2$ 
C)  $x \leq - 2$ 
D)  $y \leq - 2$

Question 14

Solve the system by using the inverse of the coefficient matrix.
-$$\begin{array} { r } 
- 3 x - 3 y - z = - 46 \
x - 9 y + 5 z = - 46 \
- 4 x + y + z = - 12
\end{array}$$

Accepted Answer

A)  $\{ ( - 6,8,12 ) \}$ 
B)  $\varnothing$ 
C)  $\{ ( 6,8,4 ) \}$ 
D)  $\{ ( 6,4,8 ) \}$ 
A)  $\{ ( - 6,8,12 ) \}$ 
B)  $\varnothing$ 
C)  $\{ ( 6,8,4 ) \}$ 
D)  $\{ ( 6,4,8 ) \}$

Question 15

Solve the equation for x.
-$\left| \begin{array} { r r r } 0 & 0 & x \ - 4 & x & - 4 \ 1 & 1 & x \end{array} \right| = 4$

Accepted Answer

A)  $\{ 5 \}$ 
B)  $\{ 2 \}$ 
C)  $\{ - 2 \}$ 
D)  $\varnothing$ 
A)  $\{ 5 \}$ 
B)  $\{ 2 \}$ 
C)  $\{ - 2 \}$ 
D)  $\varnothing$

Question 16

Use Cramerʹs rule to solve the system of equations. If D = 0, use another method to determine the solution set.
-$$\begin{array} { l } 
- 7 x - 6 y = - 44 \
- 3 x + 4 y = 14
\end{array}$$

Accepted Answer

A)  $\{ ( 1,6 ) \}$ 
B)  $\{ ( 2,5 ) \}$ 
C)  Cramer's rule does not apply since $D = 0$; 
D)  $\{ ( 2,6 ) \}$ 
A)  $\{ ( 1,6 ) \}$ 
B)  $\{ ( 2,5 ) \}$ 
C)  Cramer's rule does not apply since $D = 0$; 
D)  $\{ ( 2,6 ) \}$

Question 17

Use Cramerʹs rule to solve the system of equations. If D = 0, use another method to determine the solution set.
-$$\begin{array} { l } 
3 x + 3 y + z = 22 \
4 x - 4 y - z = 2 \
5 x + y + 3 z = 18
\end{array}$$

Accepted Answer

A)  $\{ ( 4 , - 2,4 ) \}$ 
B)  $\{ ( - 2,4,4 ) \}$ 
C)  $\{ ( 4,4 , - 2 ) \}$ 
D)  Cramer's rule does not apply since $\mathrm { D } = 0$; 
A)  $\{ ( 4 , - 2,4 ) \}$ 
B)  $\{ ( - 2,4,4 ) \}$ 
C)  $\{ ( 4,4 , - 2 ) \}$ 
D)  Cramer's rule does not apply since $\mathrm { D } = 0$;

Question 18

Find the value of the determinant.
-$\left| \begin{array} { c c } - 8 & - 4 \ b & \text { a } \end{array} \right|$

Accepted Answer

A)  $8 a - 4 b$ 
B)  $b a - 32$ 
C)  $32 - a b$ 
D)  $- 8 a + 4 b$ 
A)  $8 a - 4 b$ 
B)  $b a - 32$ 
C)  $32 - a b$ 
D)  $- 8 a + 4 b$

Question 19

Use a graphing calculator to solve the nonlinear system. Give x- and y-coordinates to the nearest hundredth.
-$$\begin{array} { l } 
y = \log ( x + 8 ) \
y = x ^ { 2 }
\end{array}$$

Accepted Answer

A)  $\{ ( - 0.92,0.85 ) , ( 0.98,0.95 ) \}$ 
B)  $\{ ( - 1.38,1.89 ) , ( 1.50,2.25 ) \}$ 
C)  $\{ ( - 0.92 , - 0.85 ) , ( 0.98 , - 0.95 ) \}$ 
D)  $\{ ( - 1.38 , - 1.89 ) , ( 1.50 , - 2.25 ) \}$ 
A)  $\{ ( - 0.92,0.85 ) , ( 0.98,0.95 ) \}$ 
B)  $\{ ( - 1.38,1.89 ) , ( 1.50,2.25 ) \}$ 
C)  $\{ ( - 0.92 , - 0.85 ) , ( 0.98 , - 0.95 ) \}$ 
D)  $\{ ( - 1.38 , - 1.89 ) , ( 1.50 , - 2.25 ) \}$

Question 20

Use a graphing calculator to find the value of the determinant.
-$\left| \begin{array} { l l l } 2 & 5 & 2 \ 3 & 2 & 1 \ 5 & 0 & 4 \end{array} \right|$

Accepted Answer

A)  121 
B)  39 
C)  $- 89$ 
D)  $- 39$ 
A)  121 
B)  39 
C)  $- 89$ 
D)  $- 39$

Solve the system. - ++= --=- ++=

Find the partial fraction decomposition for the rational expression. - $\frac { 4 x ^ { 3 } + 8 x ^ { 2 } - 6 x + 2 } { 2 x ^ { 2 } - x - 1 }$

Provide an appropriate response. -Fill in the blank to complete the statement. A matrix having the same number of rows as columns is called a? matrix.

Solve the problem. -A company makes 3 types of cable. Cable A requires 3 black, 3 white, and 2 red wires. B requires 1 black, 2 white, and 1 red. C requires 2 black, 1 white, and 2 red. The company used 100 black, 110 White and 80 red wires. How many of each type of cable were made?

Give all solutions of the nonlinear system of equations, including those with nonreal complex components. - 2-3=38 3+5=95

Write the augmented matrix for the system. Do not solve the system. - 9x+3y=78 7x+5y=58

Solve the equation for x. - $\left| \begin{array} { l l } 2 & 4 \\ \times & 3 \end{array} \right| = - 2$

Solve the system. - x+y+z=-4 x-y+4z=21 2x+y+z=-8

Use a graphing calculator to solve the system. Express solutions with approximations to the nearest thousandth. - $\sqrt { 2 } x - y = 7$ $100 x + y = 9$

Give all solutions of the nonlinear system of equations, including those with nonreal complex components. - $x ^ { 2 } - y ^ { 2 } = 39$ $x - y = 3$

Solve the system by elimination. - 4x+7y=24 -2x+2y=-12

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 by using the inverse of the coefficient matrix. - -3x-3y-z=-46 x-9y+5z=-46 -4x+y+z=-12

Solve the equation for x. - $\left| \begin{array} { r r r } 0 & 0 & x \\ - 4 & x & - 4 \\ 1 & 1 & x \end{array} \right| = 4$

Use Cramerʹs rule to solve the system of equations. If D = 0, use another method to determine the solution set. - -7x-6y=-44 -3x+4y=14

Use Cramerʹs rule to solve the system of equations. If D = 0, use another method to determine the solution set. - 3x+3y+z=22 4x-4y-z=2 5x+y+3z=18

Find the value of the determinant. - $\left| \begin{array} { c c } - 8 & - 4 \\ b & \text { a } \end{array} \right|$

Use a graphing calculator to solve the nonlinear system. Give x- and y-coordinates to the nearest hundredth. - y=(x+8) y=

Use a graphing calculator to find the value of the determinant. - $\left| \begin{array} { l l l } 2 & 5 & 2 \\ 3 & 2 & 1 \\ 5 & 0 & 4 \end{array} \right|$

Equations and Inequalities

Graphs and Functions

Polynomial and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Trigonometric Functions

The Circular Functions and Their Graphs

Trigonometric Identities and Equations

Applications of Trigonometry

Analytic Geometry

Further Topics in Algebra

Review of Basic Concepts

Filters

Exam 9: Systems and Matrices