Question 1

Find the inverse, if it exists, for the matrix.
-$$\left[ \begin{array} { r r } 
0 & - 5 \
- 1 & 5
\end{array} \right]$$

Accepted Answer

A) 
$$\left[ \begin{array} { r r } 
0 & - 1 \
- \frac { 1 } { 5 } & - 1
\end{array} \right]$$ 
B) 
$\left[\begin{array}{rr}
-1 & -1 \
-\frac{1}{5} & 0
\end{array}\right]$ 
C) 
$$\left[ \begin{array} { r r } 
- \frac { 1 } { 5 } & 0 \
- 1 & - 1
\end{array} \right]$$ 
D) 
$$\left[ \begin{array} { c c } 
- 1 & 1 \
\frac { 1 } { 5 } & 0
\end{array} \right]$$ 
A) 
$$\left[ \begin{array} { r r } 
0 & - 1 \
- \frac { 1 } { 5 } & - 1
\end{array} \right]$$ 
B) 
$\left[\begin{array}{rr}
-1 & -1 \
-\frac{1}{5} & 0
\end{array}\right]$ 
C) 
$$\left[ \begin{array} { r r } 
- \frac { 1 } { 5 } & 0 \
- 1 & - 1
\end{array} \right]$$ 
D) 
$$\left[ \begin{array} { c c } 
- 1 & 1 \
\frac { 1 } { 5 } & 0
\end{array} \right]$$

Question 2

Find the value of the determinant.
-$$\left| \begin{array} { l l } 
8 & 5 \
2 & 9
\end{array} \right|$$

Accepted Answer

A)  62 
B)  22 
C)  -62 
D)  82 
A)  62 
B)  22 
C)  -62 
D)  82

Question 3

Graph the solution set of the system of inequalities.
-$\begin{array}{l}
\frac{x^{2}}{9}-\frac{y^{2}}{16} \geq 1 \
x^{2}+y^{2} \leq 36
\end{array}$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 4

Provide an appropriate response.
-Which one of the following is a description of the graph of the solution set for the system below? $$\begin{array} { l } 
16 x ^ { 2 } + 25 y ^ { 2 } < 400 \
y < - 4
\end{array}$$

Accepted Answer

A)  Outside the ellipse and below the line 
B)  Inside the ellipse and below the line 
C)  Outside the ellipse and above the line 
D)  Inside the ellipse and above the line 
A)  Outside the ellipse and below the line 
B)  Inside the ellipse and below the line 
C)  Outside the ellipse and above the line 
D)  Inside the ellipse and above the line

Question 5

Use Cramer's rule to solve the system of equations. If D = 0, use another method to determine the solution set.
$\begin{array} { l } 
2 x + 5 y + z = - 6 \
4 x - 3 y - z = 24 \
3 x + y + 3 z = 12
\end{array}$

Accepted Answer

A)  {(4,-3,1)} 
B)  Cramer's rule does not apply since $\mathrm { D } = 0 ; \not$ 
C)   {(4,1,-3)} 
D)   {(1,-3,4)} 
A)  {(4,-3,1)} 
B)  Cramer's rule does not apply since $\mathrm { D } = 0 ; \not$ 
C)   {(4,1,-3)} 
D)   {(1,-3,4)}

Question 6

The following graph shows the populations of the metropolitan areas of City X and City Y over six years.  
-In what years was the population of the City X metropolitan area less than that of the City Y metropolitan area?

Accepted Answer

A)  Years 5-6 
B)  Years $1 - 5$ 
C)  Years 3-5 
D)  Years $1 - 3$ 
A)  Years 5-6 
B)  Years $1 - 5$ 
C)  Years 3-5 
D)  Years $1 - 3$

Question 7

Find the indicated matrix.
-Let $A = \left[ \begin{array} { l l } 1 & 3 \ 2 & 5 \end{array} \right]$ and $B = \left[ \begin{array} { r r } 0 & 4 \ - 1 & 6 \end{array} \right]$. Find $4 A + B$.

Accepted Answer

A) 
$\left[ \begin{array} { l l } 4 & 16 \ 7 & 26 \end{array} \right]$ 
B) 
$\left[ \begin{array} { r r } 4 & 7 \ 7 & 11 \end{array} \right]$ 
C) 
$\left[\begin{array}{ll}
4 & 16 \
1 & 11
\end{array}\right]$ 
D) 
$\left[\begin{array}{ll}
4 & 28 \
4 & 4
\end{array}\right]$ 
A) 
$\left[ \begin{array} { l l } 4 & 16 \ 7 & 26 \end{array} \right]$ 
B) 
$\left[ \begin{array} { r r } 4 & 7 \ 7 & 11 \end{array} \right]$ 
C) 
$\left[\begin{array}{ll}
4 & 16 \
1 & 11
\end{array}\right]$ 
D) 
$\left[\begin{array}{ll}
4 & 28 \
4 & 4
\end{array}\right]$

Question 8

Give all solutions of the nonlinear system of equations, including those with nonreal complex components.
$\begin{array} { l } 
x ^ { 2 } + x y + y ^ { 2 } = 12 \
x + y = 2
\end{array}$

Accepted Answer

A)  {(4,-2)} 
B)  {(-2,4)} 
C)  {(4,-2),(-2,4)} 
D)  {(3,-1),(-3,5)} 
A)  {(4,-2)} 
B)  {(-2,4)} 
C)  {(4,-2),(-2,4)} 
D)  {(3,-1),(-3,5)}

Question 9

Evaluate the determinant.

Accepted Answer

A)  -5 
B)  -3 
C)  129 
D)  -1 
A)  -5 
B)  -3 
C)  129 
D)  -1

Question 10

Use Cramer's rule to solve the system of equations. If D = 0, use another method to determine the solution set.
$\begin{array} { r } 
x + y + z = 9 \
2 x - 3 y + 4 z = 7
\end{array}$

Accepted Answer

A)  Cramer's rule des not apply since $\mathrm { D } = 0 ; \left\{ \left( \frac { - 7 \mathrm { z } + 34 } { 5 } , \frac { 2 \mathrm { z } - 11 } { 5 } , \mathrm { z } \right\} \right\}$ 
B)  Cramer's rule does not apply since $\mathrm { D } = 0 ; \left\{ \left\{ \frac { \mathrm { z } + 34 } { 5 } , \frac { 2 \mathrm { z } + 11 } { 5 } , \mathrm { z } \right\} \right\}$ 
C)  Cramer's rule dees not apply since $\mathrm { D } = 0 ; \left\{ \left[ \frac { - 7 \mathrm { z } + 34 } { 5 } , \frac { 2 \mathrm { z } + 11 } { 5 } , \mathrm { z } \right) \right\}$ 
D)  Cramer's rule does not apply since  D=0 ; $\varnothing$ 
A)  Cramer's rule des not apply since $\mathrm { D } = 0 ; \left\{ \left( \frac { - 7 \mathrm { z } + 34 } { 5 } , \frac { 2 \mathrm { z } - 11 } { 5 } , \mathrm { z } \right\} \right\}$ 
B)  Cramer's rule does not apply since $\mathrm { D } = 0 ; \left\{ \left\{ \frac { \mathrm { z } + 34 } { 5 } , \frac { 2 \mathrm { z } + 11 } { 5 } , \mathrm { z } \right\} \right\}$ 
C)  Cramer's rule dees not apply since $\mathrm { D } = 0 ; \left\{ \left[ \frac { - 7 \mathrm { z } + 34 } { 5 } , \frac { 2 \mathrm { z } + 11 } { 5 } , \mathrm { z } \right) \right\}$ 
D)  Cramer's rule does not apply since  D=0 ; $\varnothing$

Question 11

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)  $y \leq 2 x - 3$ 
B)  $y \leq - 2 x - 3$ 
C)  $y \geq - 2 x - 3$ 
D)  $y \geq 2 x - 3$ 
A)  $y \leq 2 x - 3$ 
B)  $y \leq - 2 x - 3$ 
C)  $y \geq - 2 x - 3$ 
D)  $y \geq 2 x - 3$

Question 12

Write the augmented matrix for the system. Do not solve the system.
$\begin{array} { r } 
8 x + 9 y = 42 \
5 y = 10
\end{array}$

Accepted Answer

A)  $\left[ \begin{array} { l l | l } 
42 & 9 & 8 \
10 & 0 & 5
\end{array} \right]$ 
B)  $\left[ \begin{array} { r r | r } 
5 & 0 & 10 \
8 & 9 & 9
\end{array} \right]$ 
C)  $\left[ \begin{array} { l l | l } 
8 & 9 & 42 \
0 & 5 & 10
\end{array} \right]$ 
D)  $\left[ \begin{array} { r r | r } 
8 & 9 & 42 \
5 & 10 & 0
\end{array} \right]$ 
A)  $\left[ \begin{array} { l l | l } 
42 & 9 & 8 \
10 & 0 & 5
\end{array} \right]$ 
B)  $\left[ \begin{array} { r r | r } 
5 & 0 & 10 \
8 & 9 & 9
\end{array} \right]$ 
C)  $\left[ \begin{array} { l l | l } 
8 & 9 & 42 \
0 & 5 & 10
\end{array} \right]$ 
D)  $\left[ \begin{array} { r r | r } 
8 & 9 & 42 \
5 & 10 & 0
\end{array} \right]$

Question 13

The solution set of the system $y _ { 1 } = 2 x + 3$ and $y _ { 2 } = - x + 9$ is $\{ ( 2,7 ) \}$. Using slopes and $y$-intercepts, determine which of the two calculator-generated screens, left or right, is the appropriate one for this system.

Accepted Answer

A)  Right 
B)  Left 
C)  Neither is correct. 
D)  Both could be correct. 
A)  Right 
B)  Left 
C)  Neither is correct. 
D)  Both could be correct.

Question 14

Which method should be used to solve the system? Explain your answer, including a description of the first step.
-$$\begin{array} { l } 
x ^ { 2 } - y ^ { 2 } = 4 \
x + 8 y = 9
\end{array}$$

Accepted Answer

Substitution should be used, b

Question 15

Solve the system by using the inverse of the coefficient matrix.
-$$\begin{array} { l } 
2 x - y - 5 z = - 3 \
3 x + 5 y + 8 z = 24 \
8 x - 8 y + z = 1
\end{array}$$

Accepted Answer

A)  $\{ ( 2,1,2 ) \}$ 
B)  $\{ ( - 2,2,4 ) \}$ 
C)  $\{ ( 2,2,1 ) \}$ 
D)  $\varnothing$ 
A)  $\{ ( 2,1,2 ) \}$ 
B)  $\{ ( - 2,2,4 ) \}$ 
C)  $\{ ( 2,2,1 ) \}$ 
D)  $\varnothing$

Question 16

Use a graphing calculator to solve the nonlinear system. Give x- and y-coordinates to the nearest hundredth.
-$$\begin{array} { l } 
x ^ { 2 } + y ^ { 2 } = 7 \
y = \sqrt [ 3 ] { x + 6 }
\end{array}$$

Accepted Answer

A)  $\{ ( - 2.13 , - 1.57 ) , ( 1.76 , - 1.98 ) \}$ 
B)  $\{ ( - 2.29 , - 1.32 ) , ( 2.29,1.32 ) \}$ 
C)  $\{ ( - 2.13,1.57 ) , ( 1.76,1.98 ) \}$ 
D)  $\{ ( - 1.76 , - 1.98 ) , ( 2.13 , - 1.57 ) \}$ 
A)  $\{ ( - 2.13 , - 1.57 ) , ( 1.76 , - 1.98 ) \}$ 
B)  $\{ ( - 2.29 , - 1.32 ) , ( 2.29,1.32 ) \}$ 
C)  $\{ ( - 2.13,1.57 ) , ( 1.76,1.98 ) \}$ 
D)  $\{ ( - 1.76 , - 1.98 ) , ( 2.13 , - 1.57 ) \}$

Question 17

Find the inverse, if it exists, for the matrix.
-$$\left[ \begin{array} { r r r r } 
5 & - 5 & 6 & - 2 \
5 & - 4 & - 2 & - 1 \
10 & - 9 & 4 & - 3 \
0 & - 10 & 12 & 0
\end{array} \right]$$

Accepted Answer

A) 
$$\left[ \begin{array} { r r r r } 
1 & 0 & 0 & - \frac { 2 } { 5 } \
0 & 1 & 0 & - \frac { 3 } { 17 } \
0 & 0 & 1 & - \frac { 5 } { 34 } \
0 & 0 & 0 & 0
\end{array} \right]$$ 
B) 
$$\left[ \begin{array} { c c c c } 
\frac { 1 } { 5 } & - \frac { 1 } { 5 } & \frac { 1 } { 6 } & - \frac { 1 } { 2 } \
\frac { 1 } { 5 } & - \frac { 1 } { 4 } & - 2 & - 1 \
\frac { 1 } { 10 } & - \frac { 1 } { 9 } & \frac { 1 } { 4 } & - \frac { 1 } { 3 } \
0 & - \frac { 1 } { 10 } & \frac { 1 } { 12 } & 0
\end{array} \right]$$ 
C)  The inverse does not exist. 
D) 
$$\left[ \begin{array} { c c c c } 
\frac { 1 } { 5 } & - \frac { 1 } { 5 } & \frac { 1 } { 6 } & - \frac { 1 } { 2 } \
\frac { 1 } { 5 } & - \frac { 1 } { 4 } & - \frac { 1 } { 2 } & - 1 \
\frac { 1 } { 10 } & - \frac { 1 } { 9 } & \frac { 1 } { 4 } & - \frac { 1 } { 3 } \
0 & - \frac { 1 } { 10 } & \frac { 1 } { 12 } & 0
\end{array} \right]$$ 
A) 
$$\left[ \begin{array} { r r r r } 
1 & 0 & 0 & - \frac { 2 } { 5 } \
0 & 1 & 0 & - \frac { 3 } { 17 } \
0 & 0 & 1 & - \frac { 5 } { 34 } \
0 & 0 & 0 & 0
\end{array} \right]$$ 
B) 
$$\left[ \begin{array} { c c c c } 
\frac { 1 } { 5 } & - \frac { 1 } { 5 } & \frac { 1 } { 6 } & - \frac { 1 } { 2 } \
\frac { 1 } { 5 } & - \frac { 1 } { 4 } & - 2 & - 1 \
\frac { 1 } { 10 } & - \frac { 1 } { 9 } & \frac { 1 } { 4 } & - \frac { 1 } { 3 } \
0 & - \frac { 1 } { 10 } & \frac { 1 } { 12 } & 0
\end{array} \right]$$ 
C)  The inverse does not exist. 
D) 
$$\left[ \begin{array} { c c c c } 
\frac { 1 } { 5 } & - \frac { 1 } { 5 } & \frac { 1 } { 6 } & - \frac { 1 } { 2 } \
\frac { 1 } { 5 } & - \frac { 1 } { 4 } & - \frac { 1 } { 2 } & - 1 \
\frac { 1 } { 10 } & - \frac { 1 } { 9 } & \frac { 1 } { 4 } & - \frac { 1 } { 3 } \
0 & - \frac { 1 } { 10 } & \frac { 1 } { 12 } & 0
\end{array} \right]$$

Question 18

Provide an appropriate response.
-Suppose that you attempt to solve a system of equations and find that $\mathrm { D } = 0$ What can you conclude about the solutions of this system?

Accepted Answer

A)  The system has exactly one solution. 
B)  The system has no solution. 
C)  The system has an infinite number of solutions. 
D)  The system has either no solution or an infinite number of solutions. 
A)  The system has exactly one solution. 
B)  The system has no solution. 
C)  The system has an infinite number of solutions. 
D)  The system has either no solution or an infinite number of solutions.

Question 19

Suppose that you are solving a system of three linear equations by the Gauss-Jordan method and obtain the following augmented matrix. $$\left[ \begin{array} { r r r | r } 
1 & - 7 & 9 & 25 \
0 & 0 & 0 & 0 \
0 & - 10 & - 9 & 23
\end{array} \right]$$ What conclusion can you draw about the solutions of the system?

Accepted Answer

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

Question 20

Evaluate the determinant.
$\left| \begin{array} { r r r } 
5 & 0 & 0 \
3 & - 2 & 0 \
- 2 & 7 & 6
\end{array} \right|$

Accepted Answer

A)   -81 
B)  60 
C)  39 
D)   -60 
A)   -81 
B)  60 
C)  39 
D)   -60

Find the inverse, if it exists, for the matrix. - $\left[ \begin{array} { r r } 0 & - 5 \\- 1 & 5\end{array} \right]$

Find the value of the determinant. - $\left| \begin{array} { l l } 8 & 5 \\2 & 9\end{array} \right|$

Graph the solution set of the system of inequalities. - -\geq1 +\leq36 $Graph the solution set of the system of inequalities. - \begin{array}{l} \frac{x^{2}}{9}-\frac{y^{2}}{16} \geq 1 \\ x^{2}+y^{2} \leq 36 \end{array}$

Provide an appropriate response. -Which one of the following is a description of the graph of the solution set for the system below? 16+25<400 y<-4

Use Cramer's rule to solve the system of equations. If D = 0, use another method to determine the solution set. 2x+5y+z=-6 4x-3y-z=24 3x+y+3z=12

The following graph shows the populations of the metropolitan areas of City X and City Y over six years. -In what years was the population of the City X metropolitan area less than that of the City Y metropolitan area?

Find the indicated matrix. -Let $A = \left[ \begin{array} { l l } 1 & 3 \\ 2 & 5 \end{array} \right]$ and $B = \left[ \begin{array} { r r } 0 & 4 \\ - 1 & 6 \end{array} \right]$ . Find $4 A + B$ .

Give all solutions of the nonlinear system of equations, including those with nonreal complex components. +xy+=12 x+y=2

Evaluate the determinant.

Use Cramer's rule to solve the system of equations. If D = 0, use another method to determine the solution set. x+y+z=9 2x-3y+4z=7

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

Write the augmented matrix for the system. Do not solve the system. 8x+9y=42 5y=10

Which method should be used to solve the system? Explain your answer, including a description of the first step. - -=4 x+8y=9

Solve the system by using the inverse of the coefficient matrix. - 2x-y-5z=-3 3x+5y+8z=24 8x-8y+z=1

Use a graphing calculator to solve the nonlinear system. Give x- and y-coordinates to the nearest hundredth. - +=7 y=

Find the inverse, if it exists, for the matrix. - $\left[ \begin{array} { r r r r } 5 & - 5 & 6 & - 2 \\5 & - 4 & - 2 & - 1 \\10 & - 9 & 4 & - 3 \\0 & - 10 & 12 & 0\end{array} \right]$

Provide an appropriate response. -Suppose that you attempt to solve a system of equations and find that $\mathrm { D } = 0$ What can you conclude about the solutions of this system?

Evaluate the determinant. $\left| \begin{array} { r r r } 5 & 0 & 0 \\3 & - 2 & 0 \\- 2 & 7 & 6\end{array} \right|$

Review of Basic Concepts

Equations and Inequalities

Graphs and Functions

Polynomials and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Arithmetic Sequence: Common Difference and First n Terms

Filters

Exam 6: Systems and Matrices

Find the inverse, if it exists, for the matrix. - [0−5−15]\left[ \begin{array} { r r } 0 & - 5 \\- 1 & 5\end{array} \right][0−1​−55​]

Find the value of the determinant. - ∣8529∣\left| \begin{array} { l l } 8 & 5 \\2 & 9\end{array} \right|​82​59​​

Graph the solution set of the system of inequalities. - -\geq1 +\leq36

Provide an appropriate response. -Which one of the following is a description of the graph of the solution set for the system below? 16+25<400 y<-4

Use Cramer's rule to solve the system of equations. If D = 0, use another method to determine the solution set. 2x+5y+z=-6 4x-3y-z=24 3x+y+3z=12

The following graph shows the populations of the metropolitan areas of City X and City Y over six years. -In what years was the population of the City X metropolitan area less than that of the City Y metropolitan area?

Find the indicated matrix. -Let A=[1325]A = \left[ \begin{array} { l l } 1 & 3 \\ 2 & 5 \end{array} \right]A=[12​35​] and B=[04−16]B = \left[ \begin{array} { r r } 0 & 4 \\ - 1 & 6 \end{array} \right]B=[0−1​46​] . Find 4A+B4 A + B4A+B .

Give all solutions of the nonlinear system of equations, including those with nonreal complex components. +xy+=12 x+y=2

Evaluate the determinant.

Use Cramer's rule to solve the system of equations. If D = 0, use another method to determine the solution set. x+y+z=9 2x-3y+4z=7

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

Write the augmented matrix for the system. Do not solve the system. 8x+9y=42 5y=10

The solution set of the system y1=2x+3y _ { 1 } = 2 x + 3y1​=2x+3 and y2=−x+9y _ { 2 } = - x + 9y2​=−x+9 is {(2,7)}\{ ( 2,7 ) \}{(2,7)} . Using slopes and yyy -intercepts, determine which of the two calculator-generated screens, left or right, is the appropriate one for this system.

Which method should be used to solve the system? Explain your answer, including a description of the first step. - -=4 x+8y=9

Solve the system by using the inverse of the coefficient matrix. - 2x-y-5z=-3 3x+5y+8z=24 8x-8y+z=1

Use a graphing calculator to solve the nonlinear system. Give x- and y-coordinates to the nearest hundredth. - +=7 y=

Find the inverse, if it exists, for the matrix. - [5−56−25−4−2−110−94−30−10120]\left[ \begin{array} { r r r r } 5 & - 5 & 6 & - 2 \\5 & - 4 & - 2 & - 1 \\10 & - 9 & 4 & - 3 \\0 & - 10 & 12 & 0\end{array} \right]​55100​−5−4−9−10​6−2412​−2−1−30​​

Provide an appropriate response. -Suppose that you attempt to solve a system of equations and find that D=0\mathrm { D } = 0D=0 What can you conclude about the solutions of this system?

Evaluate the determinant. ∣5003−20−276∣\left| \begin{array} { r r r } 5 & 0 & 0 \\3 & - 2 & 0 \\- 2 & 7 & 6\end{array} \right|​53−2​0−27​006​​

Review of Basic Concepts

Equations and Inequalities

Graphs and Functions

Polynomials and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Arithmetic Sequence: Common Difference and First n Terms

Filters

Find the inverse, if it exists, for the matrix. - $\left[ \begin{array} { r r } 0 & - 5 \\- 1 & 5\end{array} \right]$

Find the value of the determinant. - $\left| \begin{array} { l l } 8 & 5 \\2 & 9\end{array} \right|$

Graph the solution set of the system of inequalities. - -\geq1 +\leq36 $Graph the solution set of the system of inequalities. - \begin{array}{l} \frac{x^{2}}{9}-\frac{y^{2}}{16} \geq 1 \\ x^{2}+y^{2} \leq 36 \end{array}$

Find the indicated matrix. -Let $A = \left[ \begin{array} { l l } 1 & 3 \\ 2 & 5 \end{array} \right]$ and $B = \left[ \begin{array} { r r } 0 & 4 \\ - 1 & 6 \end{array} \right]$ . Find $4 A + B$ .

Find the inverse, if it exists, for the matrix. - $\left[ \begin{array} { r r r r } 5 & - 5 & 6 & - 2 \\5 & - 4 & - 2 & - 1 \\10 & - 9 & 4 & - 3 \\0 & - 10 & 12 & 0\end{array} \right]$

Provide an appropriate response. -Suppose that you attempt to solve a system of equations and find that $\mathrm { D } = 0$ What can you conclude about the solutions of this system?

Evaluate the determinant. $\left| \begin{array} { r r r } 5 & 0 & 0 \\3 & - 2 & 0 \\- 2 & 7 & 6\end{array} \right|$