Question 1

Graph the solution set of the system of inequalities.
-

Accepted Answer

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

Question 2

Graph the solution set of the system of inequalities.
-$$\begin{array} { l } 
y - x \leq 5 \
x + y \geq 3 \
y - 3 x \geq - 1
\end{array}$$

Accepted Answer

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

Question 3

Find the cofactor of the indicated element.
-a 21
$\left| \begin{array} { r r r } 1 & 2 & 3 \ - 3 & 0 & 1 \ 5 & 3 & 3 \end{array} \right|$

Accepted Answer

A)  $- 7$ 
B)  $- 3$ 
C)  3 
D)  7 
A)  $- 7$ 
B)  $- 3$ 
C)  3 
D)  7

Question 4

Use Cramerʹs rule to solve the system of equations. If D = 0, use another method to determine the solution set.
-$$\begin{array} { l } 
- 7 x + 92 = 9 y \
- 2 x - 6 y = - 40
\end{array}$$

Accepted Answer

A)  $\{ ( 7,5 ) \}$ 
B)  Cramer's rule does not apply since $D = 0 ; \varnothing$ 
C)  $\{ ( 8,5 ) \}$ 
D)  $\{ ( 8,4 ) \}$ 
A)  $\{ ( 7,5 ) \}$ 
B)  Cramer's rule does not apply since $D = 0 ; \varnothing$ 
C)  $\{ ( 8,5 ) \}$ 
D)  $\{ ( 8,4 ) \}$

Question 5

Solve the system. If the system has infinitely many solutions, write the solution set with x arbitrary.
-$$\begin{array} { l } 
3 x + 2 y + z = 4 \
2 x - 3 y - z = 5 \
5 x + 12 y + 5 z = 2
\end{array}$$

Accepted Answer

A)  $\{ ( x , - 5 x - 9 , - 13 x + 22 ) \}$ 
B)  $\{ ( x , - 5 x + 9 , - 13 x + 22 ) \}$ 
C)  $\{ ( x , 5 x - 9 , - 13 x + 22 ) \}$ 
D)  $\{ ( x , 5 x + 9 , - 13 x + 22 ) \}$ 
A)  $\{ ( x , - 5 x - 9 , - 13 x + 22 ) \}$ 
B)  $\{ ( x , - 5 x + 9 , - 13 x + 22 ) \}$ 
C)  $\{ ( x , 5 x - 9 , - 13 x + 22 ) \}$ 
D)  $\{ ( x , 5 x + 9 , - 13 x + 22 ) \}$

Question 6

Solve the system by using the inverse of the coefficient matrix.
-$$\begin{array} { l } 
- 3 x + y + 3 z - w = - 1 \
- x - 4 y + z - 2 w = - 15 \
- 4 x + 3 y - 3 z + w = 20 \
3 x - y - z - 2 w = - 6
\end{array}$$

Accepted Answer

A)  $\{ ( - 1 , - 3,2 , - 1 ) \}$ 
B)  $\{ ( - 3,4 , - 1 , - 1 ) \}$ 
C)  $\varnothing$ 
D)  $\{ ( - 1,3 , - 2,1 ) \}$ 
A)  $\{ ( - 1 , - 3,2 , - 1 ) \}$ 
B)  $\{ ( - 3,4 , - 1 , - 1 ) \}$ 
C)  $\varnothing$ 
D)  $\{ ( - 1,3 , - 2,1 ) \}$

Question 7

Decide whether or not the matrices are inverses of each other.
-$\left[ \begin{array} { r r } - 2 & 4 \ 4 & - 4 \end{array} \right]$ and $\left[ \begin{array} { l l } \frac { 1 } { 2 } & \frac { 1 } { 4 } \ \frac { 1 } { 2 } & \frac { 1 } { 4 } \end{array} \right]$

Accepted Answer

A)  Yes 
B)  $\mathrm { No }$ 
A)  Yes 
B)  $\mathrm { No }$

Question 8

Find the value of the determinant.
-$$\left| \begin{array} { r r r } 
4 & 5 & - 1 \
2 & 3 & - 3 \
- 2 & 4 & 4
\end{array} \right|$$

Accepted Answer

A)  12 
B)  72 
C)  $- 72$ 
D)  68 
A)  12 
B)  72 
C)  $- 72$ 
D)  68

Question 9

Perform the operation or operations when possible.
-$$\left[ \begin{array} { l l l } 
- 3 & 7 & 4
\end{array} \right] - \left[ \begin{array} { l l } 
4 & 3
\end{array} \right]$$

Accepted Answer

A)  $\left[ \begin{array} { l l l } - 7 & 4 & 1 \end{array} \right]$ 
B)  $\left[ \begin{array} { l l l } - 7 & 7 & 1 \end{array} \right]$ 
C)  $\left[ \begin{array} { l l l } - 7 & 4 & 4 \end{array} \right]$ 
D)  They cannot be subtracted. 
A)  $\left[ \begin{array} { l l l } - 7 & 4 & 1 \end{array} \right]$ 
B)  $\left[ \begin{array} { l l l } - 7 & 7 & 1 \end{array} \right]$ 
C)  $\left[ \begin{array} { l l l } - 7 & 4 & 4 \end{array} \right]$ 
D)  They cannot be subtracted.

Question 10

Solve the problem.
-The perimeter of a rectangle is 38 m. If the width were doubled and the length were increased by 10 m, the perimeter would be 70 m. What are the length and width of the rectangle?

Accepted Answer

A)  Length: 9 m; width: 4 m 
B)  Length: 13 m; width: 6 m 
C)  Length: 6 m; width: 13 m 
D)  Length: 9 m; width: 9 m 
A)  Length: 9 m; width: 4 m 
B)  Length: 13 m; width: 6 m 
C)  Length: 6 m; width: 13 m 
D)  Length: 9 m; width: 9 m

Question 11

Graph the solution set of the system of inequalities.
-$$\begin{array} { l } 
\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 25 } \leq 1 \
\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 9 } \leq 1
\end{array}$$

Accepted Answer

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

Question 12

Provide an appropriate response.
-Fill in the blanks to complete the statement. For a system of 2 equations and 2 unknowns, the corresponding augmented matrix will have _______ rows and _______ columns.

Accepted Answer

A)  2; 2 
B) 3; 3 
C) 3; 2 
D) 2; 3 
A)  2; 2 
B) 3; 3 
C) 3; 2 
D) 2; 3

Question 13

Provide an appropriate response.
-Fill in the blank to complete the statement. Each number in a matrix is called _______ of the matrix.

Accepted Answer

A)  an element 
B)  an expansion 
C)  a minor 
D)  a determinant 
A)  an element 
B)  an expansion 
C)  a minor 
D)  a determinant

Question 14

Solve the system by elimination.
-$$\begin{array} { l } 
x + 2 y = - 6 \
7 x + 3 y = - 42
\end{array}$$

Accepted Answer

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

Question 15

Solve the system for x and y using Cramerʹs rule. Assume a and b are nonzero constants.
-$$\begin{array} { l } 
x + b y = a ^ { 2 } \
x + a y = b ^ { 2 }
\end{array}$$

Accepted Answer

A)  $\left\{ \left( a ^ { 2 } + 2 a b + b ^ { 2 } , b - a \right) \right\}$ 
B)  $\left\{ \left( a ^ { 2 } + a b + b ^ { 2 } , a + b \right) \right\}$ 
C)  $\left\{ \left( a ^ { 2 } + 2 a b + b ^ { 2 } , - b - a \right) \right\}$ 
D)  $\left\{ \left( a ^ { 2 } + a b + b ^ { 2 } , - b - a \right) \right\}$ 
A)  $\left\{ \left( a ^ { 2 } + 2 a b + b ^ { 2 } , b - a \right) \right\}$ 
B)  $\left\{ \left( a ^ { 2 } + a b + b ^ { 2 } , a + b \right) \right\}$ 
C)  $\left\{ \left( a ^ { 2 } + 2 a b + b ^ { 2 } , - b - a \right) \right\}$ 
D)  $\left\{ \left( a ^ { 2 } + a b + b ^ { 2 } , - b - a \right) \right\}$

Question 16

Graph the solution set of the system of inequalities.
-

Accepted Answer

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

Question 17

Use Cramerʹs rule to solve the system of equations. If D = 0, use another method to determine the solution set.
-$$\begin{array} { r } 
x + y + z = - 1 \
x - y + 3 z = 7 \
3 x + y + z = - 3
\end{array}$$

Accepted Answer

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

Question 18

Use the shading capabilities of your graphing calculator to graph the inequality or system of inequalities.
-$$\begin{array} { l } 
y \leq 3 \
y \geq 2 ^ { x }
\end{array}$$

Accepted Answer

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

Question 19

Decide whether or not the matrices are inverses of each other.
-$\left[ \begin{array} { l l } - 5 & 1 \ - 7 & 1 \end{array} \right]$ and $\left[ \begin{array} { c c } \frac { 1 } { 2 } & - \frac { 1 } { 2 } \ \frac { 7 } { 2 } & - \frac { 5 } { 2 } \end{array} \right]$

Accepted Answer

A)  Yes 
B)  No 
A)  Yes 
B)  No

Question 20

The graph shows the region of feasible solutions. Find the maximum or minimum value, as specified, of the objective
function.
-objective function $= \mathrm { x } - 4 \mathrm { y }$; minimum

Accepted Answer

A)  $- 50$ 
B)  $- 38$ 
C)  $- 9$ 
D)  $- 29$ 
A)  $- 50$ 
B)  $- 38$ 
C)  $- 9$ 
D)  $- 29$

Graph the solution set of the system of inequalities. -

Graph the solution set of the system of inequalities. - y-x\leq5 x+y\geq3 y-3x\geq-1 $Graph the solution set of the system of inequalities. - \begin{array} { l } y - x \leq 5 \\ x + y \geq 3 \\ y - 3 x \geq - 1 \end{array}$

Find the cofactor of the indicated element. -a 21 $\left| \begin{array} { r r r } 1 & 2 & 3 \\ - 3 & 0 & 1 \\ 5 & 3 & 3 \end{array} \right|$

Use Cramerʹs rule to solve the system of equations. If D = 0, use another method to determine the solution set. - -7x+92=9y -2x-6y=-40

Solve the system. If the system has infinitely many solutions, write the solution set with x arbitrary. - 3x+2y+z=4 2x-3y-z=5 5x+12y+5z=2

Solve the system by using the inverse of the coefficient matrix. - -3x+y+3z-w=-1 -x-4y+z-2w=-15 -4x+3y-3z+w=20 3x-y-z-2w=-6

Decide whether or not the matrices are inverses of each other. - $\left[ \begin{array} { r r } - 2 & 4 \\ 4 & - 4 \end{array} \right]$ and $\left[ \begin{array} { l l } \frac { 1 } { 2 } & \frac { 1 } { 4 } \\ \frac { 1 } { 2 } & \frac { 1 } { 4 } \end{array} \right]$

Find the value of the determinant. - $\left| \begin{array} { r r r } 4 & 5 & - 1 \\2 & 3 & - 3 \\- 2 & 4 & 4\end{array} \right|$

Perform the operation or operations when possible. - $\left[ \begin{array} { l l l } - 3 & 7 & 4\end{array} \right] - \left[ \begin{array} { l l } 4 & 3\end{array} \right]$

Solve the problem. -The perimeter of a rectangle is 38 m. If the width were doubled and the length were increased by 10 m, the perimeter would be 70 m. What are the length and width of the rectangle?

Graph the solution set of the system of inequalities. - +\leq1 +\leq1 $Graph the solution set of the system of inequalities. - \begin{array} { l } \frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 25 } \leq 1 \\ \frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 9 } \leq 1 \end{array}$

Provide an appropriate response. -Fill in the blanks to complete the statement. For a system of 2 equations and 2 unknowns, the corresponding augmented matrix will have _ rows and _ columns.

Provide an appropriate response. -Fill in the blank to complete the statement. Each number in a matrix is called _______ of the matrix.

Solve the system by elimination. - x+2y=-6 7x+3y=-42

Solve the system for x and y using Cramerʹs rule. Assume a and b are nonzero constants. - x+by= x+ay=

Graph the solution set of the system of inequalities. -

Use Cramerʹs rule to solve the system of equations. If D = 0, use another method to determine the solution set. - x+y+z=-1 x-y+3z=7 3x+y+z=-3

Use the shading capabilities of your graphing calculator to graph the inequality or system of inequalities. - y\leq3 y\geq $Use the shading capabilities of your graphing calculator to graph the inequality or system of inequalities. - \begin{array} { l } y \leq 3 \\ y \geq 2 ^ { x } \end{array}$

Decide whether or not the matrices are inverses of each other. - $\left[ \begin{array} { l l } - 5 & 1 \\ - 7 & 1 \end{array} \right]$ and $\left[ \begin{array} { c c } \frac { 1 } { 2 } & - \frac { 1 } { 2 } \\ \frac { 7 } { 2 } & - \frac { 5 } { 2 } \end{array} \right]$

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

Graph the solution set of the system of inequalities. -

Graph the solution set of the system of inequalities. - y-x\leq5 x+y\geq3 y-3x\geq-1

Find the cofactor of the indicated element. -a 21 ∣123−301533∣\left| \begin{array} { r r r } 1 & 2 & 3 \\ - 3 & 0 & 1 \\ 5 & 3 & 3 \end{array} \right|​1−35​203​313​​

Use Cramerʹs rule to solve the system of equations. If D = 0, use another method to determine the solution set. - -7x+92=9y -2x-6y=-40

Solve the system. If the system has infinitely many solutions, write the solution set with x arbitrary. - 3x+2y+z=4 2x-3y-z=5 5x+12y+5z=2

Solve the system by using the inverse of the coefficient matrix. - -3x+y+3z-w=-1 -x-4y+z-2w=-15 -4x+3y-3z+w=20 3x-y-z-2w=-6

Find the value of the determinant. - ∣45−123−3−244∣\left| \begin{array} { r r r } 4 & 5 & - 1 \\2 & 3 & - 3 \\- 2 & 4 & 4\end{array} \right|​42−2​534​−1−34​​

Perform the operation or operations when possible. - [−374]−[43]\left[ \begin{array} { l l l } - 3 & 7 & 4\end{array} \right] - \left[ \begin{array} { l l } 4 & 3\end{array} \right][−3​7​4​]−[4​3​]

Solve the problem. -The perimeter of a rectangle is 38 m. If the width were doubled and the length were increased by 10 m, the perimeter would be 70 m. What are the length and width of the rectangle?

Graph the solution set of the system of inequalities. - +\leq1 +\leq1

Provide an appropriate response. -Fill in the blanks to complete the statement. For a system of 2 equations and 2 unknowns, the corresponding augmented matrix will have _______ rows and _______ columns.

Provide an appropriate response. -Fill in the blank to complete the statement. Each number in a matrix is called _______ of the matrix.

Solve the system by elimination. - x+2y=-6 7x+3y=-42

Solve the system for x and y using Cramerʹs rule. Assume a and b are nonzero constants. - x+by= x+ay=

Graph the solution set of the system of inequalities. -

Use Cramerʹs rule to solve the system of equations. If D = 0, use another method to determine the solution set. - x+y+z=-1 x-y+3z=7 3x+y+z=-3

Use the shading capabilities of your graphing calculator to graph the inequality or system of inequalities. - y\leq3 y\geq

The graph shows the region of feasible solutions. Find the maximum or minimum value, as specified, of the objective function. -objective function =x−4y= \mathrm { x } - 4 \mathrm { y }=x−4y ; minimum

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

Graph the solution set of the system of inequalities. - y-x\leq5 x+y\geq3 y-3x\geq-1 $Graph the solution set of the system of inequalities. - \begin{array} { l } y - x \leq 5 \\ x + y \geq 3 \\ y - 3 x \geq - 1 \end{array}$

Find the cofactor of the indicated element. -a 21 $\left| \begin{array} { r r r } 1 & 2 & 3 \\ - 3 & 0 & 1 \\ 5 & 3 & 3 \end{array} \right|$

Find the value of the determinant. - $\left| \begin{array} { r r r } 4 & 5 & - 1 \\2 & 3 & - 3 \\- 2 & 4 & 4\end{array} \right|$

Perform the operation or operations when possible. - $\left[ \begin{array} { l l l } - 3 & 7 & 4\end{array} \right] - \left[ \begin{array} { l l } 4 & 3\end{array} \right]$

Graph the solution set of the system of inequalities. - +\leq1 +\leq1 $Graph the solution set of the system of inequalities. - \begin{array} { l } \frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 25 } \leq 1 \\ \frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 9 } \leq 1 \end{array}$

Provide an appropriate response. -Fill in the blanks to complete the statement. For a system of 2 equations and 2 unknowns, the corresponding augmented matrix will have _ rows and _ columns.

Use the shading capabilities of your graphing calculator to graph the inequality or system of inequalities. - y\leq3 y\geq $Use the shading capabilities of your graphing calculator to graph the inequality or system of inequalities. - \begin{array} { l } y \leq 3 \\ y \geq 2 ^ { x } \end{array}$