Question 1

Solve the system of equations by using an inverse matrix.
-2x + 8y + 6z = 20 4x + 2y - 2z = -2
3x - y + z = 11

Accepted Answer

A)  (2, 1, 6) 
B)  (-1, 2, 1) 
C)  (2, -1, 4) 
D)  ɸ 
A)  (2, 1, 6) 
B)  (-1, 2, 1) 
C)  (2, -1, 4) 
D)  ɸ

Question 2

Determine whether the matrices are inverses.
-$$\left[ \begin{array} { r r } 
6 & - 5 \
- 3 & 5
\end{array} \right] , \left[ \begin{array} { l l } 
\frac { 1 } { 3 } & \frac { 1 } { 3 } \
\frac { 1 } { 5 } & \frac { 2 } { 5 }
\end{array} \right]$$

Accepted Answer

A) True 
 B)False

Question 3

Use Gaussian elimination to solve the system of equations.
-$$7 x - 31 = 5 y$$
$- 5 x - 3 y = - 55$

Accepted Answer

A)  $( 7,6 )$ 
B)  $( 8,5 )$ 
C)  No solution 
D)  $( 8,6 )$ 
A)  $( 7,6 )$ 
B)  $( 8,5 )$ 
C)  No solution 
D)  $( 8,6 )$

Question 4

Solve the system of inequalities.
-$\begin{aligned}
2 x+y & \geq 4 \
x-1 & \geq 0
\end{aligned}$

Accepted Answer

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

Question 5

Solve the problem.
-Find the maximum value of $f = 6 x + 7 y$ subject to the following constraints.
$$\begin{array} { l } 
2 x + 3 y \leq 12 \
2 x + y \leq 8 \
x \geq 0 \
y \geq 0
\end{array}$$

Accepted Answer

A)  Maximum of 32 
B)  Maximum of 24 
C)  Maximum of 52 
D)  Maximum of 13 
A)  Maximum of 32 
B)  Maximum of 24 
C)  Maximum of 52 
D)  Maximum of 13

Question 6

Identify the element specified for the matrix.
-$$\left[ \begin{array} { r r r r } 
9 & 4 & 5 & 9 \
- 4 & 5 & 5 & 3
\end{array} \right]$$
$\mathrm { a } _ { 12 }$

Accepted Answer

A)  4 
B)  5 
C)  9 
D)  $- 4$ 
A)  4 
B)  5 
C)  9 
D)  $- 4$

Question 7

Perform the indicated elementary row operations.
-$$\begin{array} { l } 
( - 3 ) \mathrm { R } _ { 1 } \
{ \left[ \begin{array} { r r } 
5 & 3 \
7 & - 6
\end{array} \right] }
\end{array}$$

Accepted Answer

A) 
$\left[ \begin{array} { r r } - 15 & - 9 \ 7 & - 6 \end{array} \right]$ 
B) 
$\left[ \begin{array} { r r } 15 & 9 \ 7 & - 6 \end{array} \right]$ 
C) 
$\left[ \begin{array} { l l } - 15 & - 9 \ - 21 & 18 \end{array} \right]$ 
D) 
$\left[ \begin{array} { r r } 5 & 3 \ - 21 & 18 \end{array} \right]$ 
A) 
$\left[ \begin{array} { r r } - 15 & - 9 \ 7 & - 6 \end{array} \right]$ 
B) 
$\left[ \begin{array} { r r } 15 & 9 \ 7 & - 6 \end{array} \right]$ 
C) 
$\left[ \begin{array} { l l } - 15 & - 9 \ - 21 & 18 \end{array} \right]$ 
D) 
$\left[ \begin{array} { r r } 5 & 3 \ - 21 & 18 \end{array} \right]$

Question 8

Solve the system of equations by finding the reduced row echelon form for the augmented matrix.
-$$\begin{array} { l } 
3 x + 2 y + z = 4 \
2 x - 3 y - z = 5
\end{array}$$

Accepted Answer

A)  $\left( \frac { 1 } { 13 } z + \frac { 22 } { 13 } , \frac { 5 } { 13 } z - \frac { 7 } { 13 } , z \right)$ 
B)  $\left( \frac { 1 } { 13 } z - \frac { 22 } { 13 } , \frac { 5 } { 13 } z + \frac { 7 } { 13 } , z \right)$ 
C)  $\left( - \frac { 1 } { 13 } z + \frac { 22 } { 13 } , - \frac { 5 } { 13 } z - \frac { 7 } { 13 } , z \right)$ 
D)  $\left( \frac { 22 } { 13 } z - \frac { 1 } { 13 } , - \frac { 7 } { 13 } z - \frac { 5 } { 13 } , z \right)$ 
A)  $\left( \frac { 1 } { 13 } z + \frac { 22 } { 13 } , \frac { 5 } { 13 } z - \frac { 7 } { 13 } , z \right)$ 
B)  $\left( \frac { 1 } { 13 } z - \frac { 22 } { 13 } , \frac { 5 } { 13 } z + \frac { 7 } { 13 } , z \right)$ 
C)  $\left( - \frac { 1 } { 13 } z + \frac { 22 } { 13 } , - \frac { 5 } { 13 } z - \frac { 7 } { 13 } , z \right)$ 
D)  $\left( \frac { 22 } { 13 } z - \frac { 1 } { 13 } , - \frac { 7 } { 13 } z - \frac { 5 } { 13 } , z \right)$

Question 9

Solve the system of equations.
-$$\begin{array} { c } 
x + 2 y - 3 z + w = 7 \
3 x + 4 y - z + 2 w = 4 \
- 2 x + y + z - w = - 3 \
x - y + 2 z - 2 w = 1
\end{array}$$

Accepted Answer

A)  $\left( \frac { 22 } { 35 } , \frac { 22 } { 7 } , - \frac { 22 } { 51 } , - \frac { 11 } { 24 } \right)$ 
B)  $\left( 1 , \frac { 33 } { 28 } , - \frac { 11 } { 43 } , - \frac { 33 } { 106 } \right)$ 
C)  $\left( \frac { 35 } { 22 } , \frac { 7 } { 22 } , - \frac { 51 } { 22 } , - \frac { 24 } { 11 } \right)$ 
D)  $\left( 1 , \frac { 28 } { 33 } , - \frac { 43 } { 11 } , - \frac { 106 } { 33 } \right)$ 
A)  $\left( \frac { 22 } { 35 } , \frac { 22 } { 7 } , - \frac { 22 } { 51 } , - \frac { 11 } { 24 } \right)$ 
B)  $\left( 1 , \frac { 33 } { 28 } , - \frac { 11 } { 43 } , - \frac { 33 } { 106 } \right)$ 
C)  $\left( \frac { 35 } { 22 } , \frac { 7 } { 22 } , - \frac { 51 } { 22 } , - \frac { 24 } { 11 } \right)$ 
D)  $\left( 1 , \frac { 28 } { 33 } , - \frac { 43 } { 11 } , - \frac { 106 } { 33 } \right)$

Question 10

Determine which inequality matches the graph.
-

A)$y \geq x+4$

B)$y \leq x+4$

C)$y \leq-x+4$

D)$y \geq-x+4$

Accepted Answer

The answer of Determine which inequality matches the graph.
-

A)\(y...

Question 11

Use a graph to determine the number of solutions the system has.
-$$\begin{array} { l } 
2 x - 4 y = 6 \
6 x - 12 y = 19
\end{array}$$

Accepted Answer

A)  One solution 
B)  No solution 
C)  Infinitely many solutions 
A)  One solution 
B)  No solution 
C)  Infinitely many solutions

Question 12

Solve the system of equations.
--x + 4y = -16 x - z = 1
Y + z = -10

Accepted Answer

A)  (0, -4, -1) 
B)  (-3, -6, -4) 
C)  (-4, -5, -5) 
D)  No solution 
A)  (0, -4, -1) 
B)  (-3, -6, -4) 
C)  (-4, -5, -5) 
D)  No solution

Question 13

Identify the element specified for the matrix.
-$$\left[ \begin{array} { r r r } 
0 & - 4 & 6 \
- 8 & 8 & - 5 \
4 & - 1 & 2 \
1 & 3 & - 5
\end{array} \right]$$
$a _ { 32 }$

Accepted Answer

A)  $- 1$ 
B)  $- 5$ 
C)  2 
D)  8 
A)  $- 1$ 
B)  $- 5$ 
C)  2 
D)  8

Question 14

Solve the system graphically.
-$$\begin{array} { l } 
y = 3 ^ { - x } \
y = - \frac { 3 } { x }
\end{array}$$

Accepted Answer

A)  $( - 1,3 )$ 
B)  $( 1,3 )$ 
C)  $\varnothing$ 
D)  $( 1 , - 3 )$ 
A)  $( - 1,3 )$ 
B)  $( 1,3 )$ 
C)  $\varnothing$ 
D)  $( 1 , - 3 )$

Question 15

Decide whether the ordered pair is a solution of the given system.
-(-1, 4) x + y = 5
X - y = -3

Accepted Answer

A) True 
 B)False

Question 16

Solve the problem.
-Find the minimum value of $\mathrm { f } = 2 \mathrm { x } + 4 \mathrm { y }$ subject to the following constraints.
$$\begin{array} { l } 
x + 2 y \geq 10 \
3 x + y \geq 10 \
x \geq 0 \
y \geq 0
\end{array}$$

Accepted Answer

A)  Minimum of 0 
B)  Minimum of 10 
C)  Minimum of 30 
D)  Minimum of 20 
A)  Minimum of 0 
B)  Minimum of 10 
C)  Minimum of 30 
D)  Minimum of 20

Question 17

Use division to write the rational function in the form q(x) + r(x)/d(x), where the degree of r(x) is less than the degree of
d(x). Then find the partial fraction decomposition of r(x)/d(x).
-$$\frac { x ^ { 3 } + 4 } { x ^ { 2 } + 4 x }$$

Accepted Answer

A)  $\frac { 15 } { x + 4 } + \frac { 1 } { x }$ 
B)  $x - 4 + \frac { 1 } { x + 4 } + \frac { 1 } { x }$ 
C)  $x - 4 + \frac { 15 } { x + 4 } + \frac { 1 } { x }$ 
D)  $x + 4 + \frac { 17 } { x + 4 } + \frac { 1 } { x }$ 
A)  $\frac { 15 } { x + 4 } + \frac { 1 } { x }$ 
B)  $x - 4 + \frac { 1 } { x + 4 } + \frac { 1 } { x }$ 
C)  $x - 4 + \frac { 15 } { x + 4 } + \frac { 1 } { x }$ 
D)  $x + 4 + \frac { 17 } { x + 4 } + \frac { 1 } { x }$

Question 18

Find the indicated matrix.
-Let $C = \left[ \begin{array} { r } 4 \ - 2 \ 8 \end{array} \right]$. Find $\frac { 1 } { 2 } C$

Accepted Answer

A) 
$\left[\begin{array}{r}
4 \
-1 \
8
\end{array}\right]$ 
B) 
$\left[\begin{array}{r}
8 \
-4 \
16
\end{array}\right]$ 
C) 
$\left[\begin{array}{r}
2 \
-2 \
8
\end{array}\right]$ 
D) 
$\left[\begin{array}{r}
2 \
-1 \
4
\end{array}\right]$ 
A) 
$\left[\begin{array}{r}
4 \
-1 \
8
\end{array}\right]$ 
B) 
$\left[\begin{array}{r}
8 \
-4 \
16
\end{array}\right]$ 
C) 
$\left[\begin{array}{r}
2 \
-2 \
8
\end{array}\right]$ 
D) 
$\left[\begin{array}{r}
2 \
-1 \
4
\end{array}\right]$

Question 19

Solve the system graphically.
-$$\begin{array} { l } 
y = x ^ { 2 } + 4 x - 3 \
y = 5 x + 3
\end{array}$$

Accepted Answer

A)  $\approx ( 3.00,19.50 )$ and $( - 2.00 , - 7.00 )$ 
B)  $\approx ( 3.00,18.00 )$ 
C)  $\approx ( 3.00,18.00 )$ and $( - 2.20 , - 7.00 )$ 
D)  $\approx ( 3.00,18.00 )$ and $( - 2.00 , - 7.00 )$ 
A)  $\approx ( 3.00,19.50 )$ and $( - 2.00 , - 7.00 )$ 
B)  $\approx ( 3.00,18.00 )$ 
C)  $\approx ( 3.00,18.00 )$ and $( - 2.20 , - 7.00 )$ 
D)  $\approx ( 3.00,18.00 )$ and $( - 2.00 , - 7.00 )$

Question 20

Write the augmented matrix for the system.
-

Accepted Answer

A)  $\left[ \begin{array} { r r r r } 9 & 3 & 3 & 54 \ 2 & 8 & 5 & 53 \ - 2 & 6 & 7 & 29 \end{array} \right]$ 
B)  $\left[ \begin{array} { r r r r } 54 & 3 & - 2 & 9 \ 53 & 5 & 8 & 2 \ 29 & 7 & 6 & - 2 \end{array} \right]$ 
C)  $\left[ \begin{array} { r r r } 9 & 3 & 3 \ 2 & 8 & 5 \ - 2 & 6 & 7 \end{array} \right]$ 
D)  $\left[ \begin{array} { r r r r } 9 & 2 & - 2 & 54 \ 3 & 8 & 6 & 53 \ 3 & 5 & 7 & 29 \end{array} \right]$ 
A)  $\left[ \begin{array} { r r r r } 9 & 3 & 3 & 54 \ 2 & 8 & 5 & 53 \ - 2 & 6 & 7 & 29 \end{array} \right]$ 
B)  $\left[ \begin{array} { r r r r } 54 & 3 & - 2 & 9 \ 53 & 5 & 8 & 2 \ 29 & 7 & 6 & - 2 \end{array} \right]$ 
C)  $\left[ \begin{array} { r r r } 9 & 3 & 3 \ 2 & 8 & 5 \ - 2 & 6 & 7 \end{array} \right]$ 
D)  $\left[ \begin{array} { r r r r } 9 & 2 & - 2 & 54 \ 3 & 8 & 6 & 53 \ 3 & 5 & 7 & 29 \end{array} \right]$

Solve the system of equations by using an inverse matrix. -2x + 8y + 6z = 20 4x + 2y - 2z = -2 3x - y + z = 11

Determine whether the matrices are inverses. - $\left[ \begin{array} { r r } 6 & - 5 \\- 3 & 5\end{array} \right] , \left[ \begin{array} { l l } \frac { 1 } { 3 } & \frac { 1 } { 3 } \\\frac { 1 } { 5 } & \frac { 2 } { 5 }\end{array} \right]$

Use Gaussian elimination to solve the system of equations. - $7 x - 31 = 5 y$ $- 5 x - 3 y = - 55$

Solve the system of inequalities. - 2x+y \geq4 x-1 \geq0 $Solve the system of inequalities. - \begin{aligned} 2 x+y & \geq 4 \\ x-1 & \geq 0 \end{aligned}$

Solve the problem. -Find the maximum value of $f = 6 x + 7 y$ subject to the following constraints. 2x+3y\leq12 2x+y\leq8 x\geq0 y\geq0

Identify the element specified for the matrix. - $\left[ \begin{array} { r r r r } 9 & 4 & 5 & 9 \\- 4 & 5 & 5 & 3\end{array} \right]$ $\mathrm { a } _ { 12 }$

Perform the indicated elementary row operations. - (-3) 5 3 7 -6

Solve the system of equations by finding the reduced row echelon form for the augmented matrix. - 3x+2y+z=4 2x-3y-z=5

Solve the system of equations. - x+2y-3z+w=7 3x+4y-z+2w=4 -2x+y+z-w=-3 x-y+2z-2w=1

Determine which inequality matches the graph. - $Determine which inequality matches the graph. - A) y \geq x+4 B) y \leq x+4 C) y \leq-x+4 D) y \geq-x+4$ A) $y \geq x+4$ B) $y \leq x+4$ C) $y \leq-x+4$ D) $y \geq-x+4$

Use a graph to determine the number of solutions the system has. - 2x-4y=6 6x-12y=19

Solve the system of equations. --x + 4y = -16 x - z = 1 Y + z = -10

Identify the element specified for the matrix. - $\left[ \begin{array} { r r r } 0 & - 4 & 6 \\- 8 & 8 & - 5 \\4 & - 1 & 2 \\1 & 3 & - 5\end{array} \right]$ $a _ { 32 }$

Solve the system graphically. - y= y=-

Decide whether the ordered pair is a solution of the given system. -(-1, 4) x + y = 5 X - y = -3

Solve the problem. -Find the minimum value of $\mathrm { f } = 2 \mathrm { x } + 4 \mathrm { y }$ subject to the following constraints. x+2y\geq10 3x+y\geq10 x\geq0 y\geq0

Use division to write the rational function in the form q(x) + r(x)/d(x), where the degree of r(x) is less than the degree of d(x). Then find the partial fraction decomposition of r(x)/d(x). - $\frac { x ^ { 3 } + 4 } { x ^ { 2 } + 4 x }$

Find the indicated matrix. -Let $C = \left[ \begin{array} { r } 4 \\ - 2 \\ 8 \end{array} \right]$ . Find $\frac { 1 } { 2 } C$

Solve the system graphically. - y=+4x-3 y=5x+3

Write the augmented matrix for the system. -

Functions and Graphs

Polynomial, Power, and Rational Functions

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Analytic Trigonometry

Applications of Trigonometry

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An Introduction to Calculus: Limits, Derivatives, and Integrals

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Exam 7: Systems and Matrices