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

Solve the system of equations by finding the reduced row echelon form for the augmented matrix.
-$$\begin{array} { r } 
x + 4 y + 5 z = - 27 \
4 y + 4 z = - 24 \
z = - 4
\end{array}$$

Accepted Answer

A)  $( 1 , - 2 , - 4 )$ 
B)  $( 1 , - 4 , - 2 )$ 
C)  No solution 
D)  $( - 4 , - 2,1 )$ 
A)  $( 1 , - 2 , - 4 )$ 
B)  $( 1 , - 4 , - 2 )$ 
C)  No solution 
D)  $( - 4 , - 2,1 )$

Question 3

Use a graph to determine the number of solutions the system has.
-$$\begin{array} { l } 
6 x - 9 y = 3 \
- 10 x + 15 y = 5
\end{array}$$

Accepted Answer

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

Question 4

Find the matrix product, if possible.
-$$\left[ \begin{array} { r r } 
0 & - 3 \
2 & 2
\end{array} \right] \left[ \begin{array} { l l } 
- 2 & 0 \
- 1 & 1
\end{array} \right]$$

Accepted Answer

A)

$\left[ \begin{array} { r r } - 4 & - 4 \ 2 & 5 \end{array} \right]$ 
B) 
$\left[ \begin{array} { r r } 0 & 6 \ - 2 & 2 \end{array} \right]$ 
C) 
$\left[ \begin{array} { r r } 3 & - 3 \ - 6 & 2 \end{array} \right]$ 
D) 
$\left[ \begin{array} { r r } - 3 & 3 \ - 2 & - 6 \end{array} \right]$ 
A)

$\left[ \begin{array} { r r } - 4 & - 4 \ 2 & 5 \end{array} \right]$ 
B) 
$\left[ \begin{array} { r r } 0 & 6 \ - 2 & 2 \end{array} \right]$ 
C) 
$\left[ \begin{array} { r r } 3 & - 3 \ - 6 & 2 \end{array} \right]$ 
D) 
$\left[ \begin{array} { r r } - 3 & 3 \ - 2 & - 6 \end{array} \right]$

Question 5

Determine which inequality matches the graph.
-

Accepted Answer

A)  $y \geq - x$ 
B)  $y \leq - x$ 
C)  $y \leq x$ 
D)  $\mathrm { y } \geq \mathrm { x }$ 
A)  $y \geq - x$ 
B)  $y \leq - x$ 
C)  $y \leq x$ 
D)  $\mathrm { y } \geq \mathrm { x }$

Question 6

Write the augmented matrix for the system.
-

Accepted Answer

A)  $\left[ \begin{array} { c c c c } 2 & 0 & 6 & 41 \ 0 & 5 & 6 & 35 \ 9 & 8 & 2 & - 8 \end{array} \right]$ 
B)  $\left[ \begin{array} { c c c c } 2 & 0 & 9 & 41 \ 0 & 5 & 8 & 35 \ 6 & 6 & 2 & - 8 \end{array} \right]$ 
C)  $\left[ \begin{array} { l l l } 2 & 0 & 9 \ 0 & 5 & 8 \ 6 & 6 & 2 \end{array} \right]$ 
D)  $\left[ \begin{array} { r r r r } 2 & 9 & 0 & 41 \ 5 & 8 & 0 & 35 \ 6 & 6 & 2 & - 8 \end{array} \right]$ 
A)  $\left[ \begin{array} { c c c c } 2 & 0 & 6 & 41 \ 0 & 5 & 6 & 35 \ 9 & 8 & 2 & - 8 \end{array} \right]$ 
B)  $\left[ \begin{array} { c c c c } 2 & 0 & 9 & 41 \ 0 & 5 & 8 & 35 \ 6 & 6 & 2 & - 8 \end{array} \right]$ 
C)  $\left[ \begin{array} { l l l } 2 & 0 & 9 \ 0 & 5 & 8 \ 6 & 6 & 2 \end{array} \right]$ 
D)  $\left[ \begin{array} { r r r r } 2 & 9 & 0 & 41 \ 5 & 8 & 0 & 35 \ 6 & 6 & 2 & - 8 \end{array} \right]$

Question 7

Graph the inequality.
-$$y \leq 8 ^ { x }$$

Accepted Answer

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

Question 8

Solve the system of equations by using an inverse matrix.
-$$\begin{array} { c } 
5 x + 4 y = 8 \
4 x - 2 y = 22
\end{array}$$

Accepted Answer

A)  $( 4 , - 3 )$ 
B)  $( - 4,3 )$ 
C)  $( 3 , - 4 )$ 
D)  $( - 3,4 )$ 
A)  $( 4 , - 3 )$ 
B)  $( - 4,3 )$ 
C)  $( 3 , - 4 )$ 
D)  $( - 3,4 )$

Question 9

Graph the system of inequalities. Shade the region that represents the solution set.
-$\begin{aligned}
x^{2}+y^{2} & \leq 16 \
x+y &<1
\end{aligned}$

Accepted Answer

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

Question 10

Decide whether the ordered pair is a solution of the given system.
-$$\begin{array} { l } 
( 1,3 ) \
y = x ^ { 2 } + 5 x - 3 \
y = 6 x - 3
\end{array}$$

Accepted Answer

A) True 
 B)False

Question 11

Fill in the blanks to complete the statement. For a system of 6 equations and 6 unknowns, the corresponding augmented matrix will have $?$ rows and ? columns.

Accepted Answer

A)  $7 ; 7$ 
B)  $7 ; 6$ 
C)  $6 ; 7$ 
D)  $6 ; 6$ 
A)  $7 ; 7$ 
B)  $7 ; 6$ 
C)  $6 ; 7$ 
D)  $6 ; 6$

Question 12

Solve the system of inequalities.
-$\begin{array}{r}
2 x+3 y \leq 6 \
x-y \geq 3 \
x \geq 1
\end{array}$

Accepted Answer

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

Question 13

Solve the system of equations by using an inverse matrix.
-4x + y - 2z - w = 6 -x + 4y + z - 2w = 10
4x - 2y + 4z + w = -22
-2x - y - z - 2w = 7

Accepted Answer

A)  (-1, 2, -3, -2) 
B)  ɸ 
C)  (-3, 4, -1, -4) 
D)  (-1, -2, 3, 2) 
A)  (-1, 2, -3, -2) 
B)  ɸ 
C)  (-3, 4, -1, -4) 
D)  (-1, -2, 3, 2)

Question 14

Graph the linear inequality.
-$x+y<-2$

Accepted Answer

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

Question 15

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

Accepted Answer

A) 
$\left[\begin{array}{rr}
12 & 16 \
1 & 11
\end{array}\right]$ 
B) 
$\left[\begin{array}{rr}
12 & 7 \
7 & 11
\end{array}\right]$ 
C) 
$\left[\begin{array}{rr}
12 & 16 \
7 & 26
\end{array}\right]$ 
D) 
$\left[\begin{array}{rr}
12 & 28 \
4 & 4
\end{array}\right]$ 
A) 
$\left[\begin{array}{rr}
12 & 16 \
1 & 11
\end{array}\right]$ 
B) 
$\left[\begin{array}{rr}
12 & 7 \
7 & 11
\end{array}\right]$ 
C) 
$\left[\begin{array}{rr}
12 & 16 \
7 & 26
\end{array}\right]$ 
D) 
$\left[\begin{array}{rr}
12 & 28 \
4 & 4
\end{array}\right]$

Question 16

Decide whether the ordered pair is a solution of the given system.
-$$\begin{array} { l } 
( - 1,4 ) \
y = x ^ { 2 } + 5 \
2 x + y = 4
\end{array}$$

Accepted Answer

A) True 
 B)False

Question 17

Solve the system graphically.
-$$y = e ^ { x + 3 }$$
$x ^ { 2 } - 4 y ^ { 2 } = 11$

Accepted Answer

A)  $\approx ( 2.75 , - 1.28 )$ 
B)  $\approx ( 2.75,1.28 )$ 
C)  $\approx ( - 3.52 , .59 )$ 
D)  $\approx ( 1.04 , - 0.14 )$ and $\approx ( 3.52 , - 1.69 )$ 
A)  $\approx ( 2.75 , - 1.28 )$ 
B)  $\approx ( 2.75,1.28 )$ 
C)  $\approx ( - 3.52 , .59 )$ 
D)  $\approx ( 1.04 , - 0.14 )$ and $\approx ( 3.52 , - 1.69 )$

Question 18

Find the inverse of A if it has one, or state that the inverse does not exist.
-$$A = \left[ \begin{array} { l l } 
- 5 & 0 \
- 2 & 4
\end{array} \right]$$

Accepted Answer

A)  $\left[ \begin{array} { c c } \frac { 1 } { 5 } & 0 \ - \frac { 1 } { 10 } & \frac { 1 } { 4 } \end{array} \right]$ 
B) 
$$\left[ \begin{array} { r r } 
\frac { 1 } { 4 } & 0 \
- \frac { 1 } { 10 } & - \frac { 1 } { 5 }
\end{array} \right]$$ 
C)  Inverse does not exist 
D) 
$$\left[ \begin{array} { c c } 
- \frac { 1 } { 5 } & 0 \
\frac { 1 } { 10 } & \frac { 1 } { 4 }
\end{array} \right]$$ 
A)  $\left[ \begin{array} { c c } \frac { 1 } { 5 } & 0 \ - \frac { 1 } { 10 } & \frac { 1 } { 4 } \end{array} \right]$ 
B) 
$$\left[ \begin{array} { r r } 
\frac { 1 } { 4 } & 0 \
- \frac { 1 } { 10 } & - \frac { 1 } { 5 }
\end{array} \right]$$ 
C)  Inverse does not exist 
D) 
$$\left[ \begin{array} { c c } 
- \frac { 1 } { 5 } & 0 \
\frac { 1 } { 10 } & \frac { 1 } { 4 }
\end{array} \right]$$

Question 19

Solve the problem.
-Find the equilibrium point for the given demand and supply curve. p = 4830 - 90x (demand)
P = 120x (supply)

Accepted Answer

A)  (23, 2760) 
B)  (40, 1230) 
C)  (30, 2760) 
D)  (30, 2130) 
A)  (23, 2760) 
B)  (40, 1230) 
C)  (30, 2760) 
D)  (30, 2130)

Question 20

Solve the problem.
-Find the minimum value of $\mathrm { f } = 4 \mathrm { x } + 5 \mathrm { y }$ subject to the following constraints.
$$\begin{array} { l } 
2 x - 4 y \leq 10 \
2 x + y \geq 15 \
x \geq 0 \
y \geq 0
\end{array}$$

Accepted Answer

A)  Minimum of 20 
B)  Minimum of 75 
C)  Minimum of 33 
D)  Minimum of 39 
A)  Minimum of 20 
B)  Minimum of 75 
C)  Minimum of 33 
D)  Minimum of 39

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

Solve the system of equations by finding the reduced row echelon form for the augmented matrix. - x+4y+5z=-27 4y+4z=-24 z=-4

Use a graph to determine the number of solutions the system has. - 6x-9y=3 -10x+15y=5

Find the matrix product, if possible. - $\left[ \begin{array} { r r } 0 & - 3 \\2 & 2\end{array} \right] \left[ \begin{array} { l l } - 2 & 0 \\- 1 & 1\end{array} \right]$

Determine which inequality matches the graph. -

Write the augmented matrix for the system. -

Graph the inequality. - $y \leq 8 ^ { x }$ $Graph the inequality. - y \leq 8 ^ { x }$

Solve the system of equations by using an inverse matrix. - 5x+4y=8 4x-2y=22

Graph the system of inequalities. Shade the region that represents the solution set. - + \leq16 x+y <1 $Graph the system of inequalities. Shade the region that represents the solution set. - \begin{aligned} x^{2}+y^{2} & \leq 16 \\ x+y &<1 \end{aligned}$

Decide whether the ordered pair is a solution of the given system. - (1,3) y=+5x-3 y=6x-3

Fill in the blanks to complete the statement. For a system of 6 equations and 6 unknowns, the corresponding augmented matrix will have $?$ rows and ? columns.

Solve the system of inequalities. - 2x+3y\leq6 x-y\geq3 x\geq1 $Solve the system of inequalities. - \begin{array}{r} 2 x+3 y \leq 6 \\ x-y \geq 3 \\ x \geq 1 \end{array}$

Solve the system of equations by using an inverse matrix. -4x + y - 2z - w = 6 -x + 4y + z - 2w = 10 4x - 2y + 4z + w = -22 -2x - y - z - 2w = 7

Graph the linear inequality. - $x+y<-2$

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

Decide whether the ordered pair is a solution of the given system. - (-1,4) y=+5 2x+y=4

Solve the system graphically. - $y = e ^ { x + 3 }$ $x ^ { 2 } - 4 y ^ { 2 } = 11$

Find the inverse of A if it has one, or state that the inverse does not exist. - $A = \left[ \begin{array} { l l } - 5 & 0 \\- 2 & 4\end{array} \right]$

Solve the problem. -Find the equilibrium point for the given demand and supply curve. p = 4830 - 90x (demand) P = 120x (supply)

Solve the problem. -Find the minimum value of $\mathrm { f } = 4 \mathrm { x } + 5 \mathrm { y }$ subject to the following constraints. 2x-4y\leq10 2x+y\geq15 x\geq0 y\geq0

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. -

Solve the system of equations by finding the reduced row echelon form for the augmented matrix. - x+4y+5z=-27 4y+4z=-24 z=-4

Use a graph to determine the number of solutions the system has. - 6x-9y=3 -10x+15y=5

Find the matrix product, if possible. - [0−322][−20−11]\left[ \begin{array} { r r } 0 & - 3 \\2 & 2\end{array} \right] \left[ \begin{array} { l l } - 2 & 0 \\- 1 & 1\end{array} \right][02​−32​][−2−1​01​]

Determine which inequality matches the graph. -

Write the augmented matrix for the system. -

Graph the inequality. - y≤8xy \leq 8 ^ { x }y≤8x

Solve the system of equations by using an inverse matrix. - 5x+4y=8 4x-2y=22

Graph the system of inequalities. Shade the region that represents the solution set. - + \leq16 x+y <1

Decide whether the ordered pair is a solution of the given system. - (1,3) y=+5x-3 y=6x-3

Fill in the blanks to complete the statement. For a system of 6 equations and 6 unknowns, the corresponding augmented matrix will have ??? rows and ? columns.

Solve the system of inequalities. - 2x+3y\leq6 x-y\geq3 x\geq1

Solve the system of equations by using an inverse matrix. -4x + y - 2z - w = 6 -x + 4y + z - 2w = 10 4x - 2y + 4z + w = -22 -2x - y - z - 2w = 7

Graph the linear inequality. - x+y<−2x+y<-2x+y<−2

Find the indicated matrix. -Let A=[3325]\mathrm { A } = \left[ \begin{array} { l l } 3 & 3 \\ 2 & 5 \end{array} \right]A=[32​35​] and B=[04−16]\mathrm { B } = \left[ \begin{array} { r r } 0 & 4 \\ - 1 & 6 \end{array} \right]B=[0−1​46​] . Find 4 A+B4 \mathrm {~A} + \mathrm { B }4 A+B .

Decide whether the ordered pair is a solution of the given system. - (-1,4) y=+5 2x+y=4

Solve the system graphically. - y=ex+3y = e ^ { x + 3 }y=ex+3 x2−4y2=11x ^ { 2 } - 4 y ^ { 2 } = 11x2−4y2=11

Find the inverse of A if it has one, or state that the inverse does not exist. - A=[−50−24]A = \left[ \begin{array} { l l } - 5 & 0 \\- 2 & 4\end{array} \right]A=[−5−2​04​]

Solve the problem. -Find the equilibrium point for the given demand and supply curve. p = 4830 - 90x (demand) P = 120x (supply)

Solve the problem. -Find the minimum value of f=4x+5y\mathrm { f } = 4 \mathrm { x } + 5 \mathrm { y }f=4x+5y subject to the following constraints. 2x-4y\leq10 2x+y\geq15 x\geq0 y\geq0

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 matrix product, if possible. - $\left[ \begin{array} { r r } 0 & - 3 \\2 & 2\end{array} \right] \left[ \begin{array} { l l } - 2 & 0 \\- 1 & 1\end{array} \right]$

Graph the inequality. - $y \leq 8 ^ { x }$ $Graph the inequality. - y \leq 8 ^ { x }$

Graph the system of inequalities. Shade the region that represents the solution set. - + \leq16 x+y <1 $Graph the system of inequalities. Shade the region that represents the solution set. - \begin{aligned} x^{2}+y^{2} & \leq 16 \\ x+y &<1 \end{aligned}$

Fill in the blanks to complete the statement. For a system of 6 equations and 6 unknowns, the corresponding augmented matrix will have $?$ rows and ? columns.

Solve the system of inequalities. - 2x+3y\leq6 x-y\geq3 x\geq1 $Solve the system of inequalities. - \begin{array}{r} 2 x+3 y \leq 6 \\ x-y \geq 3 \\ x \geq 1 \end{array}$

Graph the linear inequality. - $x+y<-2$

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

Solve the system graphically. - $y = e ^ { x + 3 }$ $x ^ { 2 } - 4 y ^ { 2 } = 11$

Find the inverse of A if it has one, or state that the inverse does not exist. - $A = \left[ \begin{array} { l l } - 5 & 0 \\- 2 & 4\end{array} \right]$

Solve the problem. -Find the minimum value of $\mathrm { f } = 4 \mathrm { x } + 5 \mathrm { y }$ subject to the following constraints. 2x-4y\leq10 2x+y\geq15 x\geq0 y\geq0