Question 1

Solve the system by substitution.
-x + 6y = 0 x - 6y = 96

Accepted Answer

A)  (-8, 48) 
B)  (6, -1) 
C)  (48, -8) 
D)  (48, 8) 
A)  (-8, 48) 
B)  (6, -1) 
C)  (48, -8) 
D)  (48, 8)

Question 2

Determine which elementary row operation(s) applied to the first matrix will yield the second matrix.
-

Accepted Answer

The answer of Determine which elementary row operation(s) applied to...

Question 3

Solve the problem.
-A basketball field house seats 15,000. Courtside seats sell for $9, end zone for $7, and balcony for $4. The total for a sell-out is $81,000. If half the courtside and balcony and all end zone seats are sold, ticket sales total
$47,500. How many of each type of seat are there?

Accepted Answer

A)  4000 courtside 
B)  3000 courtside 
C)  3200 courtside 3000 end zone 2000 end zone 1800 end zone
8000 balcony 10,000 balcony 10,000 balcony 
A)  4000 courtside 
B)  3000 courtside 
C)  3200 courtside 3000 end zone 2000 end zone 1800 end zone
8000 balcony 10,000 balcony 10,000 balcony

Question 4

Determine which inequality matches the graph.
-

Accepted Answer

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

Question 5

2x - 7y = -17
5x + 3y = 19
If your friend was going to solve this system of equations by first eliminating y, what general suggestions
would you make so your friend could start on this in a systematic way?

Accepted Answer

Answers may vary. One possibility: Multi

Question 6

Solve the system of equations by using an inverse matrix.
-$$\begin{array} { l } 
- 5 x + 3 y = 8 \
2 x - 4 y = - 20
\end{array}$$
$2 x - 4 y = - 20$

Accepted Answer

A)  $( - 2 , - 6 )$ 
B)  $( 6,2 )$ 
C)  $( 2,6 )$ 
D)  $( - 6 , - 2 )$ 
A)  $( - 2 , - 6 )$ 
B)  $( 6,2 )$ 
C)  $( 2,6 )$ 
D)  $( - 6 , - 2 )$

Question 7

Find a matrix A and a column matrix B that describe the following tables involving credits and tuition costs. Find the
matrix product AB, and interpret the significance of the entries of this product.
-

Accepted Answer

A) 
$$\mathrm { AB } = \left[ \begin{array} { r } 
960 \
810 \
1011
\end{array} \right]$$
Tuition for Student 1 is $\$ 960$, tuition for Student 2 is $\$ 810$, and tuition for Student 3 is $\$ 1011$. 
B) 
$\mathrm { AB } = [ 63 ]$
The average cost per credit hour is $\$ 63$. 
C) 
$$\mathrm { AB } = \left[ \begin{array} { r } 
1074 \
981 \
726
\end{array} \right]$$
Tuition for Student 1 is $\$ 1074$, tuition for Student 2 is $\$ 981$, and tuition for Student 3 is $\$ 726$. 
D) 
$$\mathrm { AB } = \left[ \begin{array} { r } 
789 \
1095 \
897
\end{array} \right]$$
Tuition for Student 1 is $\$ 789$, tuition for Student 2 is $\$ 1095$, and tuition for Student 3 is $\$ 897$. 
A) 
$$\mathrm { AB } = \left[ \begin{array} { r } 
960 \
810 \
1011
\end{array} \right]$$
Tuition for Student 1 is $\$ 960$, tuition for Student 2 is $\$ 810$, and tuition for Student 3 is $\$ 1011$. 
B) 
$\mathrm { AB } = [ 63 ]$
The average cost per credit hour is $\$ 63$. 
C) 
$$\mathrm { AB } = \left[ \begin{array} { r } 
1074 \
981 \
726
\end{array} \right]$$
Tuition for Student 1 is $\$ 1074$, tuition for Student 2 is $\$ 981$, and tuition for Student 3 is $\$ 726$. 
D) 
$$\mathrm { AB } = \left[ \begin{array} { r } 
789 \
1095 \
897
\end{array} \right]$$
Tuition for Student 1 is $\$ 789$, tuition for Student 2 is $\$ 1095$, and tuition for Student 3 is $\$ 897$.

Question 8

Solve the problem.
-Use inverse matrices to find the equilibrium point for the demand and supply curves below.
$p = 100 - 10 x \quad$ Demand curve
$p = 30 + 5 x \quad$ Supply curve

Accepted Answer

A)  $\left( \frac { 20 } { 3 } , \frac { 190 } { 3 } \right)$ 
B)  $( 70,380 )$ 
C)  $\left( \frac { 14 } { 3 } , \frac { 160 } { 3 } \right)$ 
D)  $\left( \frac { 26 } { 3 } , \frac { 220 } { 3 } \right)$ 
A)  $\left( \frac { 20 } { 3 } , \frac { 190 } { 3 } \right)$ 
B)  $( 70,380 )$ 
C)  $\left( \frac { 14 } { 3 } , \frac { 160 } { 3 } \right)$ 
D)  $\left( \frac { 26 } { 3 } , \frac { 220 } { 3 } \right)$

Question 9

Determine which elementary row operation(s) applied to the first matrix will yield the second matrix.
-

Accepted Answer

The answer of Determine which elementary row operation(s) applied to...

Question 10

Solve the system of equations.
-x + 2y + z + 6w = 2 x + y + 2z + w = 2
X + y + z + 2w = -1

Accepted Answer

A)  (w - 7, -4w + 3, w + 3, w) 
B)  (w - 7, -4w + 3, -w + 3, w) 
C)  No solution 
D)  (-7w + 7, 4w + 3, w + 3, w) 
A)  (w - 7, -4w + 3, w + 3, w) 
B)  (w - 7, -4w + 3, -w + 3, w) 
C)  No solution 
D)  (-7w + 7, 4w + 3, w + 3, w)

Question 11

Identify the element specified for the matrix.
-$$\left[ \begin{array} { r r r r r } 
- 6 & 1 & 2 & 8 & 0 \
- 4 & 7 & - 1 & 0 & 2 \
8 & 0 & - 1 & - 2 & 3 \
- 2 & - 6 & - 8 & - 6 & 8
\end{array} \right]$$
$a _ { 13 }$

Accepted Answer

A)  8 
B)  $- 6$ 
C)  2 
D)  $- 1$ 
A)  8 
B)  $- 6$ 
C)  2 
D)  $- 1$

Question 12

Find the matrix product, if possible.
-$$\text { [ } \left. \begin{array} { l l l } 
- 6 & - 9 & 1 ]
\end{array} \right] \left[ \begin{array} { r r r } 
2 & - 2 & - 2 \
- 1 & - 8 & - 3 \
- 2 & - 6 & 1
\end{array} \right]$$

Accepted Answer

A) 
$$\left[ \begin{array} { r r r } 
- 6 & - 9 & 1 \
2 & - 2 & - 2 \
- 1 & - 8 & - 3 \
- 2 & - 6 & 1
\end{array} \right]$$ 
B) 
$\left[\begin{array}{rrr}
-12 & 18 & -2 \
6 & 72 & -3 \
12 & 54 & 1
\end{array}\right]$ 
C) 
$\left[\begin{array}{r}
-5 \
78 \
40
\end{array}\right]$ 
D) 
[-5 7840 ] 
A) 
$$\left[ \begin{array} { r r r } 
- 6 & - 9 & 1 \
2 & - 2 & - 2 \
- 1 & - 8 & - 3 \
- 2 & - 6 & 1
\end{array} \right]$$ 
B) 
$\left[\begin{array}{rrr}
-12 & 18 & -2 \
6 & 72 & -3 \
12 & 54 & 1
\end{array}\right]$ 
C) 
$\left[\begin{array}{r}
-5 \
78 \
40
\end{array}\right]$ 
D) 
[-5 7840 ]

Question 13

Find a row echelon form or a reduced row echelon form, as indicated, for the given matrix.
-Find a reduced row echelon form for the matrix.

Accepted Answer

The answer of Find a row echelon form or a...

Question 14

Find a matrix A and a column matrix B that describe the following tables involving credits and tuition costs. Find the
matrix product AB, and interpret the significance of the entries of this product.
-

Accepted Answer

A)  $\mathrm { AB } = \left[ \begin{array} { r } 1068 \ 924 \end{array} \right]$
Tuition for Student 2 is $\$ 1068$ and tuition for Student 1 is $\$ 924$. 
B)  $A B = \left[ \begin{array} { r } 1083 \ 941 \end{array} \right]$
Tuition for Student 1 is $\$ 1083$ and tuition for Student 2 is $\$ 941$. 
C)  $\mathrm { AB } = \left[ \begin{array} { r } 1068 \ 924 \end{array} \right]$
Tuition for Student 1 is $\$ 1068$ and tuition for Student 2 is $\$ 924$. 
D)  $\mathrm { AB } = \left[ \begin{array} { r } 1083 \ 941 \end{array} \right]$
Tuition for Student 2 is $\$ 1083$ and tuition for Student 1 is $\$ 941$. 
A)  $\mathrm { AB } = \left[ \begin{array} { r } 1068 \ 924 \end{array} \right]$
Tuition for Student 2 is $\$ 1068$ and tuition for Student 1 is $\$ 924$. 
B)  $A B = \left[ \begin{array} { r } 1083 \ 941 \end{array} \right]$
Tuition for Student 1 is $\$ 1083$ and tuition for Student 2 is $\$ 941$. 
C)  $\mathrm { AB } = \left[ \begin{array} { r } 1068 \ 924 \end{array} \right]$
Tuition for Student 1 is $\$ 1068$ and tuition for Student 2 is $\$ 924$. 
D)  $\mathrm { AB } = \left[ \begin{array} { r } 1083 \ 941 \end{array} \right]$
Tuition for Student 2 is $\$ 1083$ and tuition for Student 1 is $\$ 941$.

Question 15

Solve the problem.
-In one study the maximum heart rates of conditioned athletes were examined. A group of athletes was exercised to exhaustion. Let x represent an athlete's heart rate five seconds after stopping exercise and y represent an athlete's heart
Rate ten seconds after stopping exercise. It was found that the maximum heart rate H for these athletes satisfied the
Following two equations.
H = 0.491 x + 0.468 y + 11.2
H = -0.981 x + 1.872y + 26.4
If an athlete had a maximum heart rate of H = 160, determine the value of x graphically to the tenths place.

Accepted Answer

A)  x = 157.3 
B)  x = 157.0 
C)  x = 156.2 
D)  x = 156.7 
A)  x = 157.3 
B)  x = 157.0 
C)  x = 156.2 
D)  x = 156.7

Question 16

Find a row echelon form or a reduced row echelon form, as indicated, for the given matrix.
-Find a row echelon form for the matrix.

Accepted Answer

The answer of Find a row echelon form or a...

Question 17

Solve the system of equations by using an inverse matrix.
-x - 2y + 3z = 11 4x + y - z = 4
2x - y + 3z = 10

Accepted Answer

A)  (-2, -3, 3) 
B)  ɸ 
C)  (2, -3, 1) 
D)  (2, 3, 5) 
A)  (-2, -3, 3) 
B)  ɸ 
C)  (2, -3, 1) 
D)  (2, 3, 5)

Question 18

Determine which elementary row operation(s) applied to the first matrix will yield the second matrix.
-

Accepted Answer

The answer of Determine which elementary row operation(s) applied to...

Question 19

Find the indicated matrix product or state that the product is undefined.
-$$A = \left[ \begin{array} { l } 
- 1 \
- 8 \
- 6
\end{array} \right] , B = \left[ \begin{array} { r r r } 
4 & - 8 & 2 \
8 & 8 & - 7
\end{array} \right]$$
$\mathrm { AB }$

Accepted Answer

A) 
$\left[\begin{array}{rrr}
-4 & 8 & -2 \
-64 & -64 & 56
\end{array}\right]$ 
B) 
$\left[\begin{array}{r}
48 \
-30
\end{array}\right]$ 
C) 
$\left[\begin{array}{ll}
48 & -30
\end{array}\right]$ 
D)  Undefined 
A) 
$\left[\begin{array}{rrr}
-4 & 8 & -2 \
-64 & -64 & 56
\end{array}\right]$ 
B) 
$\left[\begin{array}{r}
48 \
-30
\end{array}\right]$ 
C) 
$\left[\begin{array}{ll}
48 & -30
\end{array}\right]$ 
D)  Undefined

Question 20

Find the indicated matrix product or state that the product is undefined.
-$$
A=\left[\begin{array}{l}
-8 \
-1 \
-5 \
-9
\end{array}\right], B=\left[\begin{array}{rcc}
0 & 3 & -2 \
-5 & 1 & 6 \
-4 & -1 & 0
\end{array}\right]
$$
BA

Accepted Answer

A) 
$$
\left[\begin{array}{rrr}
0 & -24 & 16 \
5 & -1 & -6 \
-45 & 5 & 0
\end{array}\right]
$$ 
B)  $ \left[\begin{array}{lll}25 & 125 & 10\end{array}\right] $ 
C)  Undefined 
D)

$$
\left[\begin{array}{r}
7 \
9 \
33
\end{array}\right]
$$ 
A) 
$$
\left[\begin{array}{rrr}
0 & -24 & 16 \
5 & -1 & -6 \
-45 & 5 & 0
\end{array}\right]
$$ 
B)  $ \left[\begin{array}{lll}25 & 125 & 10\end{array}\right] $ 
C)  Undefined 
D)

$$
\left[\begin{array}{r}
7 \
9 \
33
\end{array}\right]
$$

Solve the system by substitution. -x + 6y = 0 x - 6y = 96

Determine which elementary row operation(s) applied to the first matrix will yield the second matrix. -

Solve the problem. -A basketball field house seats 15,000. Courtside seats sell for $9, end zone for $7, and balcony for $4. The total for a sell-out is $81,000. If half the courtside and balcony and all end zone seats are sold, ticket sales total $47,500. How many of each type of seat are there?

Determine which inequality matches the graph. -

2x - 7y = -17 5x + 3y = 19 If your friend was going to solve this system of equations by first eliminating y, what general suggestions would you make so your friend could start on this in a systematic way?

Solve the system of equations by using an inverse matrix. - -5x+3y=8 2x-4y=-20 $2 x - 4 y = - 20$

Find a matrix A and a column matrix B that describe the following tables involving credits and tuition costs. Find the matrix product AB, and interpret the significance of the entries of this product. -

Solve the problem. -Use inverse matrices to find the equilibrium point for the demand and supply curves below. $p = 100 - 10 x \quad$ Demand curve $p = 30 + 5 x \quad$ Supply curve

Determine which elementary row operation(s) applied to the first matrix will yield the second matrix. -

Solve the system of equations. -x + 2y + z + 6w = 2 x + y + 2z + w = 2 X + y + z + 2w = -1

Identify the element specified for the matrix. - $\left[ \begin{array} { r r r r r } - 6 & 1 & 2 & 8 & 0 \\- 4 & 7 & - 1 & 0 & 2 \\8 & 0 & - 1 & - 2 & 3 \\- 2 & - 6 & - 8 & - 6 & 8\end{array} \right]$ $a _ { 13 }$

Find the matrix product, if possible. - $\text { [ } \left. \begin{array} { l l l } - 6 & - 9 & 1 ]\end{array} \right] \left[ \begin{array} { r r r } 2 & - 2 & - 2 \\- 1 & - 8 & - 3 \\- 2 & - 6 & 1\end{array} \right]$

Find a row echelon form or a reduced row echelon form, as indicated, for the given matrix. -Find a reduced row echelon form for the matrix.

Find a matrix A and a column matrix B that describe the following tables involving credits and tuition costs. Find the matrix product AB, and interpret the significance of the entries of this product. -

Find a row echelon form or a reduced row echelon form, as indicated, for the given matrix. -Find a row echelon form for the matrix.

Solve the system of equations by using an inverse matrix. -x - 2y + 3z = 11 4x + y - z = 4 2x - y + 3z = 10

Determine which elementary row operation(s) applied to the first matrix will yield the second matrix. -

Find the indicated matrix product or state that the product is undefined. - $A = \left[ \begin{array} { l } - 1 \\- 8 \\- 6\end{array} \right] , B = \left[ \begin{array} { r r r } 4 & - 8 & 2 \\8 & 8 & - 7\end{array} \right]$ $\mathrm { AB }$

Find the indicated matrix product or state that the product is undefined. - $A=\left[\begin{array}{l}-8 \\-1 \\-5 \\-9\end{array}\right], B=\left[\begin{array}{rcc}0 & 3 & -2 \\-5 & 1 & 6 \\-4 & -1 & 0\end{array}\right]$ BA

Functions and Graphs

Polynomial, Power, and Rational Functions

Exponential, Logistic, and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometry

Analytic Geometry in Two and Three Dimensions

Discrete Mathematics

Statistics and Probability

An Introduction to Calculus: Limits, Derivatives, and Integrals

Prerequisites

Filters

Exam 7: Systems and Matrices

Solve the system by substitution. -x + 6y = 0 x - 6y = 96

Determine which elementary row operation(s) applied to the first matrix will yield the second matrix. -

Solve the problem. -A basketball field house seats 15,000. Courtside seats sell for $9, end zone for $7, and balcony for $4. The total for a sell-out is $81,000. If half the courtside and balcony and all end zone seats are sold, ticket sales total $47,500. How many of each type of seat are there?

Determine which inequality matches the graph. -

2x - 7y = -17 5x + 3y = 19 If your friend was going to solve this system of equations by first eliminating y, what general suggestions would you make so your friend could start on this in a systematic way?

Solve the system of equations by using an inverse matrix. - -5x+3y=8 2x-4y=-20 2x−4y=−202 x - 4 y = - 202x−4y=−20

Find a matrix A and a column matrix B that describe the following tables involving credits and tuition costs. Find the matrix product AB, and interpret the significance of the entries of this product. -

Solve the problem. -Use inverse matrices to find the equilibrium point for the demand and supply curves below. p=100−10xp = 100 - 10 x \quadp=100−10x Demand curve p=30+5xp = 30 + 5 x \quadp=30+5x Supply curve

Determine which elementary row operation(s) applied to the first matrix will yield the second matrix. -

Solve the system of equations. -x + 2y + z + 6w = 2 x + y + 2z + w = 2 X + y + z + 2w = -1

Find a row echelon form or a reduced row echelon form, as indicated, for the given matrix. -Find a reduced row echelon form for the matrix.

Find a matrix A and a column matrix B that describe the following tables involving credits and tuition costs. Find the matrix product AB, and interpret the significance of the entries of this product. -

Find a row echelon form or a reduced row echelon form, as indicated, for the given matrix. -Find a row echelon form for the matrix.

Solve the system of equations by using an inverse matrix. -x - 2y + 3z = 11 4x + y - z = 4 2x - y + 3z = 10

Determine which elementary row operation(s) applied to the first matrix will yield the second matrix. -

Functions and Graphs

Polynomial, Power, and Rational Functions

Exponential, Logistic, and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometry

Analytic Geometry in Two and Three Dimensions

Discrete Mathematics

Statistics and Probability

An Introduction to Calculus: Limits, Derivatives, and Integrals

Prerequisites

Filters

Solve the system of equations by using an inverse matrix. - -5x+3y=8 2x-4y=-20 $2 x - 4 y = - 20$

Solve the problem. -Use inverse matrices to find the equilibrium point for the demand and supply curves below. $p = 100 - 10 x \quad$ Demand curve $p = 30 + 5 x \quad$ Supply curve