Question 1

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 2

Find the partial fraction decomposition.
-$$\frac { x + 2 } { x ^ { 2 } - 1 } = \frac { A } { x + 1 } + \frac { B } { x - 1 }$$

Accepted Answer

A)  $\mathrm { A } = - \frac { 1 } { 2 } , \mathrm {~B} = \frac { 3 } { 2 }$ 
B)  $\mathrm { A } = \frac { 1 } { 2 } , \mathrm {~B} = - \frac { 3 } { 2 }$ 
C)  $A = - \frac { 1 } { 2 } , B = - \frac { 3 } { 2 }$ 
D)  $\mathrm { A } = \frac { 1 } { 2 } , \mathrm {~B} = \frac { 3 } { 2 }$ 
A)  $\mathrm { A } = - \frac { 1 } { 2 } , \mathrm {~B} = \frac { 3 } { 2 }$ 
B)  $\mathrm { A } = \frac { 1 } { 2 } , \mathrm {~B} = - \frac { 3 } { 2 }$ 
C)  $A = - \frac { 1 } { 2 } , B = - \frac { 3 } { 2 }$ 
D)  $\mathrm { A } = \frac { 1 } { 2 } , \mathrm {~B} = \frac { 3 } { 2 }$

Question 3

Suppose that you are solving a system of 4 linear equations in 4 variables by the row echelon method. If you use the transformation $2 R _ { 1 } + R _ { 2 }$, which row or rows of the augmented matrix, if any, will change?

Accepted Answer

A)  Rows 1 and 2 
B)  Row 1 
C)  Row 2 
D)  None 
A)  Rows 1 and 2 
B)  Row 1 
C)  Row 2 
D)  None

Question 4

Solve the system of equations by finding the reduced row echelon form for the augmented matrix.
-$$\begin{array} { c } 
x + y + z = 1 \
x - y + 4 z = 16 \
2 x + y + z = 2
\end{array}$$

Accepted Answer

A)  $( 1 , - 3,3 )$ 
B)  $( 3,1 , - 3 )$ 
C)  $( 3 , - 3,1 )$ 
D)  No solution 
A)  $( 1 , - 3,3 )$ 
B)  $( 3,1 , - 3 )$ 
C)  $( 3 , - 3,1 )$ 
D)  No solution

Question 5

Graph the linear inequality.
-$x \geq 2$

Accepted Answer

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

Question 6

Solve the problem.
-The sum of three numbers is 2 . The first, minus the second, plus 4 times the third, is 21 . The third, plus 5 times the first, plus the second, is $- 2$. What are the numbers?

Accepted Answer

A)  $( - 1 , - 1 , - 2 )$ 
B)  $( 1,2 , - 5 )$ 
C)  No solution 
D)  $( - 1 , - 2,5 )$ 
A)  $( - 1 , - 1 , - 2 )$ 
B)  $( 1,2 , - 5 )$ 
C)  No solution 
D)  $( - 1 , - 2,5 )$

Question 7

Solve the problem.
-An airline with two types of airplanes, $\mathrm { P } _ { 1 }$ and $\mathrm { P } _ { 2 }$, has contracted with a tour group to provide transportation for a minimum of 400 first class, 900 tourist class, and 1500 economy class passengers. For a certain trip, airplane $\mathrm { P } _ { 1 }$ costs $\$ 10,000$ to operate and can accommodate 20 first class, 50 tourist class, and 110 economy class passengers. Airplane $\mathrm { P } _ { 2 }$ costs $\$ 8500$ to operate and can accommodate 18 first class, 30 tourist class, and 44 economy class passengers. How many of each type of airplane should be used in order to minimize the operating cost?

Accepted Answer

A)  $9 \mathrm { P } _ { 1 }$ planes and $13 \mathrm { P } _ { 2 }$ planes 
B)  $14 \mathrm { P } _ { 1 }$ planes and $7 \mathrm { P } _ { 2 }$ planes 
C)  $5 \mathrm { P } _ { 1 }$ planes and $22 \mathrm { P } _ { 2 }$ planes 
D)  $13 \mathrm { P } _ { 1 }$ planes and $9 \mathrm { P } _ { 2 }$ planes 
A)  $9 \mathrm { P } _ { 1 }$ planes and $13 \mathrm { P } _ { 2 }$ planes 
B)  $14 \mathrm { P } _ { 1 }$ planes and $7 \mathrm { P } _ { 2 }$ planes 
C)  $5 \mathrm { P } _ { 1 }$ planes and $22 \mathrm { P } _ { 2 }$ planes 
D)  $13 \mathrm { P } _ { 1 }$ planes and $9 \mathrm { P } _ { 2 }$ planes

Question 8

Graph the inequality.
-$$x ^ { 2 } + y ^ { 2 } \geq 25$$

Accepted Answer

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

Question 9

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

Accepted Answer

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

Question 10

Perform the indicated operation, if possible.
-$\left[ \begin{array} { l l } 3 & 4 \end{array} \right] + \left[ \begin{array} { r } - 2 \ 9 \end{array} \right]$

Accepted Answer

A) 
$\left[ \begin{array} { l l } 1 & 13 \end{array} \right]$ 
B) 
$\left[\begin{array}{rr}
3 & -2 \
4 & 9
\end{array}\right]$ 
C)  $\left[\begin{array}{r}
1 \
13
\end{array}\right]$ 
D)  Not defined 
A) 
$\left[ \begin{array} { l l } 1 & 13 \end{array} \right]$ 
B) 
$\left[\begin{array}{rr}
3 & -2 \
4 & 9
\end{array}\right]$ 
C)  $\left[\begin{array}{r}
1 \
13
\end{array}\right]$ 
D)  Not defined

Question 11

Solve the system by substitution.
-x + y = 3 x - y = 1

Accepted Answer

A)  (2, 1) 
B)  No solution 
C)  (1, 2) 
D)  (-2, 2) 
A)  (2, 1) 
B)  No solution 
C)  (1, 2) 
D)  (-2, 2)

Question 12

Find the indicated matrix product or state that the product is undefined.
-$$A = \left[ \begin{array} { l } 
9 \
9
\end{array} \right] , B = \left[ \begin{array} { r r } 
5 & 2 \
- 6 & 3
\end{array} \right]$$
$\mathrm { AB }$

Accepted Answer

A)  Undefined 
B) 
$$\left[ \begin{array} { r r } 
45 & 18 \
- 54 & 27
\end{array} \right]$$ 
C) 
$$\left[ \begin{array} { r } 
63 \
- 27
\end{array} \right]$$ 
D) 
$\left[ \begin{array} { l l } - 9 & 45 \end{array} \right]$ 
A)  Undefined 
B) 
$$\left[ \begin{array} { r r } 
45 & 18 \
- 54 & 27
\end{array} \right]$$ 
C) 
$$\left[ \begin{array} { r } 
63 \
- 27
\end{array} \right]$$ 
D) 
$\left[ \begin{array} { l l } - 9 & 45 \end{array} \right]$

Question 13

Solve the system algebraically.
-$$\begin{array} { l } 
y = 3 x ^ { 2 } \
2 x + y = 8
\end{array}$$

Accepted Answer

A)  $\left( - \frac { 4 } { 3 } , \frac { 16 } { 3 } \right)$ and $( - 2,12 )$ 
B)  $\left( \frac { 4 } { 3 } , \frac { 16 } { 3 } \right)$ and $( - 2,12 )$ 
C)  $\left( \frac { 4 } { 3 } , \frac { 16 } { 3 } \right)$ and $( 2,12 )$ 
D)  $\left( - \frac { 4 } { 3 } , \frac { 16 } { 3 } \right)$ and $( 2,12 )$ 
A)  $\left( - \frac { 4 } { 3 } , \frac { 16 } { 3 } \right)$ and $( - 2,12 )$ 
B)  $\left( \frac { 4 } { 3 } , \frac { 16 } { 3 } \right)$ and $( - 2,12 )$ 
C)  $\left( \frac { 4 } { 3 } , \frac { 16 } { 3 } \right)$ and $( 2,12 )$ 
D)  $\left( - \frac { 4 } { 3 } , \frac { 16 } { 3 } \right)$ and $( 2,12 )$

Question 14

Graph the inequality.
-$$x ^ { 2 } + ( y + 3 ) ^ { 2 } \leq 4$$

Accepted Answer

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

Question 15

Graph the linear inequality.
-$-2 x-5 y \leq-10$

Accepted Answer

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

Question 16

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) 
$$\mathrm { AB } = \left[ \begin{array} { r } 
1064 \
813 \
796
\end{array} \right]$$
Tuition for Student 1 is $\$ 1064$, tuition for Student 2 is $\$ 813$, and tuition for Student 3 is $\$ 796$. 
B) 
$$\mathrm { AB } = \left[ \begin{array} { r } 
1057 \
815 \
782
\end{array} \right]$$
Tuition for Student 1 is $\$ 1057$, tuition for Student 2 is $\$ 815$, and tuition for Student 3 is $\$ 782$. 
C) 
$$\mathrm { AB } = \left[ \begin{array} { l l l } 
1074 & 799 & 804
\end{array} \right]$$
Tuition for Student 1 is $\$ 1074$, tuition for Student 2 is $\$ 799$, and tuition for Student 3 is $\$ 804$. 
D) 
$$\mathrm { AB } = \left[ \begin{array} { l l l } 
1063 & 815 & 806
\end{array} \right]$$
Tuition for Student 1 is $\$ 1063$, tuition for Student 2 is $\$ 815$, and tuition for Student 3 is $\$ 806$. 
A) 
$$\mathrm { AB } = \left[ \begin{array} { r } 
1064 \
813 \
796
\end{array} \right]$$
Tuition for Student 1 is $\$ 1064$, tuition for Student 2 is $\$ 813$, and tuition for Student 3 is $\$ 796$. 
B) 
$$\mathrm { AB } = \left[ \begin{array} { r } 
1057 \
815 \
782
\end{array} \right]$$
Tuition for Student 1 is $\$ 1057$, tuition for Student 2 is $\$ 815$, and tuition for Student 3 is $\$ 782$. 
C) 
$$\mathrm { AB } = \left[ \begin{array} { l l l } 
1074 & 799 & 804
\end{array} \right]$$
Tuition for Student 1 is $\$ 1074$, tuition for Student 2 is $\$ 799$, and tuition for Student 3 is $\$ 804$. 
D) 
$$\mathrm { AB } = \left[ \begin{array} { l l l } 
1063 & 815 & 806
\end{array} \right]$$
Tuition for Student 1 is $\$ 1063$, tuition for Student 2 is $\$ 815$, and tuition for Student 3 is $\$ 806$.

Question 17

Graph the inequality.
-$$( x - 4 ) ^ { 2 } + ( y + 3 ) ^ { 2 } \leq 16$$

Accepted Answer

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

Question 18

Determine the order of the matrix.
-$$\left[ \begin{array} { c c c } 
2 & 0 & 4 \
- 1 & 6 & - 6 \
0 & 9 & - 4
\end{array} \right]$$

Accepted Answer

A)  $3 \times 3$ 
B)  $6 \times 6$ 
C)  $2 \times 3$ 
D)  9 
A)  $3 \times 3$ 
B)  $6 \times 6$ 
C)  $2 \times 3$ 
D)  9

Question 19

Suppose that you are solving a system of three linear equations in three variables by the row echelon method ans obtain the following augmented matrix.
$$\left[ \begin{array} { l r r r } 
1 & - 12 & - 18 & 12 \
0 & 1 & - 5 & 10 \
0 & - 20 & - 11 & 3
\end{array} \right]$$
What row transformation would you perform next?

Accepted Answer

A)  Add 20 times row 1 to $- 12$ times row 3 . 
B)  Multiply row 3 by $- \frac { 1 } { 11 }$. 
C)  Add $- \frac { 1 } { 20 }$ times row 2 to row 3 . 
D)  Add 20 times row 2 to row $3 .$ 
A)  Add 20 times row 1 to $- 12$ times row 3 . 
B)  Multiply row 3 by $- \frac { 1 } { 11 }$. 
C)  Add $- \frac { 1 } { 20 }$ times row 2 to row 3 . 
D)  Add 20 times row 2 to row $3 .$

Question 20

Determine the value of each variable.
-$\left[ \begin{array} { r r r } - 5 & 1 & x \ 7 & y & - 4 \end{array} \right] = \left[ \begin{array} { r r r } m & 1 & 2 \ n & 4 & p \end{array} \right]$

Accepted Answer

A)  $m = - 5 , x = 2 , n = 1 , y = 4 , p = - 4$ 
B)  $\mathrm { m } = 7 , \mathrm { x } = 1 , \mathrm { n } = - 5 , \mathrm { y } = 4 , \mathrm { p } = - 4$ 
C)  $m = - 5 , x = 2 , n = 7 , y = 4 , p = - 4$ 
D)  $m = - 5 , x = 1 , n = 7 , y = 4 , p = - 4$ 
A)  $m = - 5 , x = 2 , n = 1 , y = 4 , p = - 4$ 
B)  $\mathrm { m } = 7 , \mathrm { x } = 1 , \mathrm { n } = - 5 , \mathrm { y } = 4 , \mathrm { p } = - 4$ 
C)  $m = - 5 , x = 2 , n = 7 , y = 4 , p = - 4$ 
D)  $m = - 5 , x = 1 , n = 7 , y = 4 , p = - 4$

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

Find the partial fraction decomposition. - $\frac { x + 2 } { x ^ { 2 } - 1 } = \frac { A } { x + 1 } + \frac { B } { x - 1 }$

Suppose that you are solving a system of 4 linear equations in 4 variables by the row echelon method. If you use the transformation $2 R _ { 1 } + R _ { 2 }$ , which row or rows of the augmented matrix, if any, will change?

Solve the system of equations by finding the reduced row echelon form for the augmented matrix. - x+y+z=1 x-y+4z=16 2x+y+z=2

Graph the linear inequality. - $x \geq 2$ $Graph the linear inequality. - x \geq 2$

Solve the problem. -The sum of three numbers is 2 . The first, minus the second, plus 4 times the third, is 21 . The third, plus 5 times the first, plus the second, is $- 2$ . What are the numbers?

Graph the inequality. - $x ^ { 2 } + y ^ { 2 } \geq 25$ $Graph the inequality. - x ^ { 2 } + y ^ { 2 } \geq 25$

Solve the system of inequalities. - 2x+y\leq4 x-1\geq0 $Solve the system of inequalities. - \begin{array}{r} 2 x+y \leq 4 \\ x-1 \geq 0 \end{array}$

Perform the indicated operation, if possible. - $\left[ \begin{array} { l l } 3 & 4 \end{array} \right] + \left[ \begin{array} { r } - 2 \\ 9 \end{array} \right]$

Solve the system by substitution. -x + y = 3 x - y = 1

Find the indicated matrix product or state that the product is undefined. - $A = \left[ \begin{array} { l } 9 \\9\end{array} \right] , B = \left[ \begin{array} { r r } 5 & 2 \\- 6 & 3\end{array} \right]$ $\mathrm { AB }$

Solve the system algebraically. - y=3 2x+y=8

Graph the inequality. - $x ^ { 2 } + ( y + 3 ) ^ { 2 } \leq 4$ $Graph the inequality. - x ^ { 2 } + ( y + 3 ) ^ { 2 } \leq 4$

Graph the linear inequality. - $-2 x-5 y \leq-10$ $Graph the linear inequality. - -2 x-5 y \leq-10$

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. -

Graph the inequality. - $( x - 4 ) ^ { 2 } + ( y + 3 ) ^ { 2 } \leq 16$ $Graph the inequality. - ( x - 4 ) ^ { 2 } + ( y + 3 ) ^ { 2 } \leq 16$

Determine the order of the matrix. - $\left[ \begin{array} { c c c } 2 & 0 & 4 \\- 1 & 6 & - 6 \\0 & 9 & - 4\end{array} \right]$

Determine the value of each variable. - $\left[ \begin{array} { r r r } - 5 & 1 & x \\ 7 & y & - 4 \end{array} \right] = \left[ \begin{array} { r r r } m & 1 & 2 \\ n & 4 & p \end{array} \right]$

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

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

Find the partial fraction decomposition. - x+2x2−1=Ax+1+Bx−1\frac { x + 2 } { x ^ { 2 } - 1 } = \frac { A } { x + 1 } + \frac { B } { x - 1 }x2−1x+2​=x+1A​+x−1B​

Suppose that you are solving a system of 4 linear equations in 4 variables by the row echelon method. If you use the transformation 2R1+R22 R _ { 1 } + R _ { 2 }2R1​+R2​ , which row or rows of the augmented matrix, if any, will change?

Solve the system of equations by finding the reduced row echelon form for the augmented matrix. - x+y+z=1 x-y+4z=16 2x+y+z=2

Graph the linear inequality. - x≥2x \geq 2x≥2

Solve the problem. -The sum of three numbers is 2 . The first, minus the second, plus 4 times the third, is 21 . The third, plus 5 times the first, plus the second, is −2- 2−2 . What are the numbers?

Graph the inequality. - x2+y2≥25x ^ { 2 } + y ^ { 2 } \geq 25x2+y2≥25

Solve the system of inequalities. - 2x+y\leq4 x-1\geq0

Perform the indicated operation, if possible. - [34]+[−29]\left[ \begin{array} { l l } 3 & 4 \end{array} \right] + \left[ \begin{array} { r } - 2 \\ 9 \end{array} \right][3​4​]+[−29​]

Solve the system by substitution. -x + y = 3 x - y = 1

Find the indicated matrix product or state that the product is undefined. - A=[99],B=[52−63]A = \left[ \begin{array} { l } 9 \\9\end{array} \right] , B = \left[ \begin{array} { r r } 5 & 2 \\- 6 & 3\end{array} \right]A=[99​],B=[5−6​23​] AB\mathrm { AB }AB

Solve the system algebraically. - y=3 2x+y=8

Graph the inequality. - x2+(y+3)2≤4x ^ { 2 } + ( y + 3 ) ^ { 2 } \leq 4x2+(y+3)2≤4

Graph the linear inequality. - −2x−5y≤−10-2 x-5 y \leq-10−2x−5y≤−10

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. -

Graph the inequality. - (x−4)2+(y+3)2≤16( x - 4 ) ^ { 2 } + ( y + 3 ) ^ { 2 } \leq 16(x−4)2+(y+3)2≤16

Determine the order of the matrix. - [204−16−609−4]\left[ \begin{array} { c c c } 2 & 0 & 4 \\- 1 & 6 & - 6 \\0 & 9 & - 4\end{array} \right]​2−10​069​4−6−4​​

Determine the value of each variable. - [−51x7y−4]=[m12n4p]\left[ \begin{array} { r r r } - 5 & 1 & x \\ 7 & y & - 4 \end{array} \right] = \left[ \begin{array} { r r r } m & 1 & 2 \\ n & 4 & p \end{array} \right][−57​1y​x−4​]=[mn​14​2p​]

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

Find the partial fraction decomposition. - $\frac { x + 2 } { x ^ { 2 } - 1 } = \frac { A } { x + 1 } + \frac { B } { x - 1 }$

Suppose that you are solving a system of 4 linear equations in 4 variables by the row echelon method. If you use the transformation $2 R _ { 1 } + R _ { 2 }$ , which row or rows of the augmented matrix, if any, will change?

Graph the linear inequality. - $x \geq 2$ $Graph the linear inequality. - x \geq 2$

Solve the problem. -The sum of three numbers is 2 . The first, minus the second, plus 4 times the third, is 21 . The third, plus 5 times the first, plus the second, is $- 2$ . What are the numbers?

Graph the inequality. - $x ^ { 2 } + y ^ { 2 } \geq 25$ $Graph the inequality. - x ^ { 2 } + y ^ { 2 } \geq 25$

Solve the system of inequalities. - 2x+y\leq4 x-1\geq0 $Solve the system of inequalities. - \begin{array}{r} 2 x+y \leq 4 \\ x-1 \geq 0 \end{array}$

Perform the indicated operation, if possible. - $\left[ \begin{array} { l l } 3 & 4 \end{array} \right] + \left[ \begin{array} { r } - 2 \\ 9 \end{array} \right]$

Find the indicated matrix product or state that the product is undefined. - $A = \left[ \begin{array} { l } 9 \\9\end{array} \right] , B = \left[ \begin{array} { r r } 5 & 2 \\- 6 & 3\end{array} \right]$ $\mathrm { AB }$

Graph the inequality. - $x ^ { 2 } + ( y + 3 ) ^ { 2 } \leq 4$ $Graph the inequality. - x ^ { 2 } + ( y + 3 ) ^ { 2 } \leq 4$

Graph the linear inequality. - $-2 x-5 y \leq-10$ $Graph the linear inequality. - -2 x-5 y \leq-10$

Graph the inequality. - $( x - 4 ) ^ { 2 } + ( y + 3 ) ^ { 2 } \leq 16$ $Graph the inequality. - ( x - 4 ) ^ { 2 } + ( y + 3 ) ^ { 2 } \leq 16$

Determine the order of the matrix. - $\left[ \begin{array} { c c c } 2 & 0 & 4 \\- 1 & 6 & - 6 \\0 & 9 & - 4\end{array} \right]$

Determine the value of each variable. - $\left[ \begin{array} { r r r } - 5 & 1 & x \\ 7 & y & - 4 \end{array} \right] = \left[ \begin{array} { r r r } m & 1 & 2 \\ n & 4 & p \end{array} \right]$