Question 1

Graph the linear inequality.
-$y \leq-3$

Accepted Answer

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

Question 2

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

Accepted Answer

(-10)R1

Question 3

Write the augmented matrix for the system.
-

Accepted Answer

A)  $\left[ \begin{array} { r r r } 4 & 2 & 14 \ 9 & 45 & 0 \end{array} \right]$ 
B)  $\left[ \begin{array} { l l l } 14 & 2 & 4 \ 45 & 0 & 9 \end{array} \right]$ 
C)  $\left[ \begin{array} { l l l } 4 & 2 & 14 \ 0 & 9 & 45 \end{array} \right]$ 
D)  $\left[ \begin{array} { r r r } 9 & 0 & 45 \ 4 & 2 & 2 \end{array} \right]$ 
A)  $\left[ \begin{array} { r r r } 4 & 2 & 14 \ 9 & 45 & 0 \end{array} \right]$ 
B)  $\left[ \begin{array} { l l l } 14 & 2 & 4 \ 45 & 0 & 9 \end{array} \right]$ 
C)  $\left[ \begin{array} { l l l } 4 & 2 & 14 \ 0 & 9 & 45 \end{array} \right]$ 
D)  $\left[ \begin{array} { r r r } 9 & 0 & 45 \ 4 & 2 & 2 \end{array} \right]$ C

Question 4

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 5

Find the inverse of A if it has one, or state that the inverse does not exist.
-$$A = \left[ \begin{array} { r r r } 
1 & 0 & 0 \
- 1 & 1 & 0 \
1 & 1 & 1
\end{array} \right]$$

Accepted Answer

A)  Inverse does not exist 
B) 
$$\left[ \begin{array} { r r r } 
1 & 0 & 0 \
1 & 1 & 0 \
- 2 & - 1 & 1
\end{array} \right]$$ 
C) 
$$\left[ \begin{array} { r r r } 
- 1 & 0 & 0 \
- 1 & - 1 & 0 \
- 1 & - 1 & - 1
\end{array} \right]$$ 
D) 
$$\left[ \begin{array} { l l l } 
1 & 1 & 1 \
0 & 1 & 1 \
0 & 0 & 1
\end{array} \right]$$ 
A)  Inverse does not exist 
B) 
$$\left[ \begin{array} { r r r } 
1 & 0 & 0 \
1 & 1 & 0 \
- 2 & - 1 & 1
\end{array} \right]$$ 
C) 
$$\left[ \begin{array} { r r r } 
- 1 & 0 & 0 \
- 1 & - 1 & 0 \
- 1 & - 1 & - 1
\end{array} \right]$$ 
D) 
$$\left[ \begin{array} { l l l } 
1 & 1 & 1 \
0 & 1 & 1 \
0 & 0 & 1
\end{array} \right]$$

Question 6

Solve the system by substitution.
-x - 5y = -1 y = 1

Accepted Answer

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

Question 7

Determine the value of each variable.
-$$\left[ \begin{array} { r r r } 
- 1 & 9 & - 6 \
1 & \mathrm {~m} & - 2
\end{array} \right] = \left[ \begin{array} { r r r } 
\mathrm { x } & \mathrm { y } & - 6 \
1 & - 6 & - 2
\end{array} \right]$$

Accepted Answer

A)  $x = 1 ; y = 9 ; m = 6$ 
B)  $x = 1 ; y = - 9 ; m = 6$ 
C)  $x = - 1 ; y = 9 ; m = - 6$ 
D)  $x = 9 ; y = - 1 ; m = - 6$ 
A)  $x = 1 ; y = 9 ; m = 6$ 
B)  $x = 1 ; y = - 9 ; m = 6$ 
C)  $x = - 1 ; y = 9 ; m = - 6$ 
D)  $x = 9 ; y = - 1 ; m = - 6$

Question 8

Determine the value of each variable.
-$\left[ \begin{array} { l l } 0 & 0 \ \mathrm { a } & \mathrm { b } \end{array} \right] = \left[ \begin{array} { r r } 0 & \mathrm { q } \ 6 & - 2 \end{array} \right]$

Accepted Answer

A)  $a = 0 ; b = 0 ; q = 0$ 
B)  $a = - 6 ; b = 2 ; q = 0$ 
C)  $a = 6 ; b = - 2 ; q = 0$ 
D)  $a = - 2 ; b = 6 ; q = 0$ 
A)  $a = 0 ; b = 0 ; q = 0$ 
B)  $a = - 6 ; b = 2 ; q = 0$ 
C)  $a = 6 ; b = - 2 ; q = 0$ 
D)  $a = - 2 ; b = 6 ; q = 0$

Question 9

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, 750 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)  $11 \mathrm { P } _ { 1 }$ planes and $7 \mathrm { P } _ { 2 }$ planes 
B)  $7 \mathrm { P } _ { 1 }$ planes and $11 \mathrm { P } _ { 2 }$ planes 
C)  $9 \mathrm { P } _ { 1 }$ planes and $13 \mathrm { P } _ { 2 }$ planes 
D)  $5 \mathrm { P } _ { 1 }$ planes and $17 \mathrm { P } _ { 2 }$ planes 
A)  $11 \mathrm { P } _ { 1 }$ planes and $7 \mathrm { P } _ { 2 }$ planes 
B)  $7 \mathrm { P } _ { 1 }$ planes and $11 \mathrm { P } _ { 2 }$ planes 
C)  $9 \mathrm { P } _ { 1 }$ planes and $13 \mathrm { P } _ { 2 }$ planes 
D)  $5 \mathrm { P } _ { 1 }$ planes and $17 \mathrm { P } _ { 2 }$ planes

Question 10

Graph the system of inequalities. Shade the region that represents the solution set.
-$$\begin{aligned}
y & \leq \sqrt { x + 4 } \
x + y & > - 3
\end{aligned}$$

Accepted Answer

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

Question 11

Solve the problem.
-A certain area of forest is populated by two species of animals, which scientists refer to as A and B for simplicity. The forest supplies two kinds of food, referred to as $\mathrm { F } _ { 1 }$ and $\mathrm { F } _ { 2 }$. For one year, species A requires $1.4$ units of $\mathrm { F } _ { 1 }$ and $0.95$ units of $\mathrm { F } _ { 2 }$. Species $\mathrm { B }$ requires $2.1$ units of $\mathrm { F } _ { 1 }$ and $1.7$ units of $\mathrm { F } _ { 2 }$. The forest can normally supply at most 938 units of $\mathrm { F } _ { 1 }$ and 492 units of $\mathrm { F } _ { 2 }$ per year. What is the maximum total number of these animals that the forest can support?

Accepted Answer

A)  209 animals 
B)  351 animals 
C)  517 animals 
D)  1021 animals 
A)  209 animals 
B)  351 animals 
C)  517 animals 
D)  1021 animals

Question 12

Use Gaussian elimination to solve the system of equations.
-x + 4y + 5z = 9 4y + 2z = -10
Z = 5

Accepted Answer

A)  No solution 
B)  (4, -5, 5) 
C)  (5, -5, 4) 
D)  (4, 5, -5) 
A)  No solution 
B)  (4, -5, 5) 
C)  (5, -5, 4) 
D)  (4, 5, -5)

Question 13

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

Accepted Answer

A)  $\left( \frac { 3 - 2 \sqrt { 11 } } { 5 } , \frac { 6 - \sqrt { 11 } } { 5 } \right)$ and $\left( \frac { 3 + 2 \sqrt { 11 } } { 5 } , \frac { 6 + \sqrt { 11 } } { 5 } \right)$ 
B)  $\left\{ \frac { 3 - 2 \sqrt { 11 } } { 5 } , \frac { 6 + \sqrt { 11 } } { 5 } \right)$ and $\left( \frac { 3 + 2 \sqrt { 11 } } { 5 } , \frac { 6 - \sqrt { 11 } } { 5 } \right)$ 
C)  $\left\{ \frac { 9 - 2 \sqrt { 11 } } { 5 } , \frac { 6 + 2 \sqrt { 11 } } { 5 } \right)$ and $\left( \frac { 9 + 2 \sqrt { 11 } } { 5 } , \frac { 6 - 2 \sqrt { 11 } } { 5 } \right)$ 
D)  $\left( \frac { 3 - 4 \sqrt { 11 } } { 5 } , \frac { 6 + 2 \sqrt { 11 } } { 5 } \right)$ and $\left( \frac { 3 + 4 \sqrt { 11 } } { 5 } , \frac { 6 - 2 \sqrt { 11 } } { 5 } \right)$ 
A)  $\left( \frac { 3 - 2 \sqrt { 11 } } { 5 } , \frac { 6 - \sqrt { 11 } } { 5 } \right)$ and $\left( \frac { 3 + 2 \sqrt { 11 } } { 5 } , \frac { 6 + \sqrt { 11 } } { 5 } \right)$ 
B)  $\left\{ \frac { 3 - 2 \sqrt { 11 } } { 5 } , \frac { 6 + \sqrt { 11 } } { 5 } \right)$ and $\left( \frac { 3 + 2 \sqrt { 11 } } { 5 } , \frac { 6 - \sqrt { 11 } } { 5 } \right)$ 
C)  $\left\{ \frac { 9 - 2 \sqrt { 11 } } { 5 } , \frac { 6 + 2 \sqrt { 11 } } { 5 } \right)$ and $\left( \frac { 9 + 2 \sqrt { 11 } } { 5 } , \frac { 6 - 2 \sqrt { 11 } } { 5 } \right)$ 
D)  $\left( \frac { 3 - 4 \sqrt { 11 } } { 5 } , \frac { 6 + 2 \sqrt { 11 } } { 5 } \right)$ and $\left( \frac { 3 + 4 \sqrt { 11 } } { 5 } , \frac { 6 - 2 \sqrt { 11 } } { 5 } \right)$

Question 14

Consider the equation 5(-3 - x) + x = 14x - 5(3 - x). Now consider the following system of equations solvable by the
substitution method:
y = 5(-3 - x) + x
y = 14x - 5(3 - x).
Explain the connections that exist between the single equation and the system of two equations.

Accepted Answer

Answers may vary. One possibility: The l

Question 15

Use Gaussian elimination to solve the system of equations.
-$$\begin{array} { l } 
x + y + z = 2 \
x - y + 5 z = - 22 \
2 x + y + z = 7
\end{array}$$

Accepted Answer

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

Question 16

Determine which inequality matches the graph.
-

Accepted Answer

The answer of Determine which inequality matches the graph.
- ...

Question 17

Perform the indicated operation, if possible.
-$$\left[ \begin{array} { r r } 
- 2 & 1 \
2 & 5
\end{array} \right] + \left[ \begin{array} { l l } 
6 & 2 \
1 & 3
\end{array} \right]$$

Accepted Answer

A) 
$\left[ \begin{array} { l l } 3 & 4 \ 4 & 8 \end{array} \right]$ 
B) 
$[ 18 ]$ 
C) 
$\left[ \begin{array} { l l } 4 & 3 \ 3 & 8 \end{array} \right]$ 
D) 
$\left[ \begin{array} { r r } 4 & 0 \ - 1 & 1 \end{array} \right]$ 
A) 
$\left[ \begin{array} { l l } 3 & 4 \ 4 & 8 \end{array} \right]$ 
B) 
$[ 18 ]$ 
C) 
$\left[ \begin{array} { l l } 4 & 3 \ 3 & 8 \end{array} \right]$ 
D) 
$\left[ \begin{array} { r r } 4 & 0 \ - 1 & 1 \end{array} \right]$

Question 18

Determine the order of the matrix.
-$$\left[ \begin{array} { r } 
2 \
- 1 \
2
\end{array} \right]$$

Accepted Answer

A)  3 
B)  $1 \times 3$ 
C)  1 
D)  $3 \times 1$ 
A)  3 
B)  $1 \times 3$ 
C)  1 
D)  $3 \times 1$

Question 19

Graph the inequality.
-$(x-5)^{2}+(y+4)^{2} \leq 4$

Accepted Answer

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

Question 20

Answer the question.
-Find $a , b$, and $c$ so that the graph of the equation $y = a x ^ { 2 } + b x + c$ passes through the points $( 5 , - 104 ) , ( 5 , - 104 )$, and $( 2 , - 26 )$.

Accepted Answer

A)  $y = - 3 x ^ { 2 } - 5 x - 4$ 
B)  $y = 3 x ^ { 2 } - 5 x - 4$ 
C)  $y = - 3 x ^ { 2 } - 5 x + 4$ 
D)  $y = - 3 x ^ { 2 } + 5 x - 4$ 
A)  $y = - 3 x ^ { 2 } - 5 x - 4$ 
B)  $y = 3 x ^ { 2 } - 5 x - 4$ 
C)  $y = - 3 x ^ { 2 } - 5 x + 4$ 
D)  $y = - 3 x ^ { 2 } + 5 x - 4$

Graph the linear inequality. - $y \leq-3$ $Graph the linear inequality. - y \leq-3$

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

Write the augmented matrix for the system. -

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 the inverse of A if it has one, or state that the inverse does not exist. - $A = \left[ \begin{array} { r r r } 1 & 0 & 0 \\- 1 & 1 & 0 \\1 & 1 & 1\end{array} \right]$

Solve the system by substitution. -x - 5y = -1 y = 1

Determine the value of each variable. - $\left[ \begin{array} { r r r } - 1 & 9 & - 6 \\1 & \mathrm {~m} & - 2\end{array} \right] = \left[ \begin{array} { r r r } \mathrm { x } & \mathrm { y } & - 6 \\1 & - 6 & - 2\end{array} \right]$

Determine the value of each variable. - $\left[ \begin{array} { l l } 0 & 0 \\ \mathrm { a } & \mathrm { b } \end{array} \right] = \left[ \begin{array} { r r } 0 & \mathrm { q } \\ 6 & - 2 \end{array} \right]$

Graph the system of inequalities. Shade the region that represents the solution set. - y \leq x+y >-3 $Graph the system of inequalities. Shade the region that represents the solution set. - \begin{aligned} y & \leq \sqrt { x + 4 } \\ x + y & > - 3 \end{aligned}$

Use Gaussian elimination to solve the system of equations. -x + 4y + 5z = 9 4y + 2z = -10 Z = 5

Solve the system algebraically. - +=4 x+2y=3

Consider the equation 5(-3 - x) + x = 14x - 5(3 - x). Now consider the following system of equations solvable by the substitution method: y = 5(-3 - x) + x y = 14x - 5(3 - x). Explain the connections that exist between the single equation and the system of two equations.

Use Gaussian elimination to solve the system of equations. - x+y+z=2 x-y+5z=-22 2x+y+z=7

Determine which inequality matches the graph. -

Perform the indicated operation, if possible. - $\left[ \begin{array} { r r } - 2 & 1 \\2 & 5\end{array} \right] + \left[ \begin{array} { l l } 6 & 2 \\1 & 3\end{array} \right]$

Determine the order of the matrix. - $\left[ \begin{array} { r } 2 \\- 1 \\2\end{array} \right]$

Graph the inequality. - $(x-5)^{2}+(y+4)^{2} \leq 4$ $Graph the inequality. - (x-5)^{2}+(y+4)^{2} \leq 4$

Answer the question. -Find $a , b$ , and $c$ so that the graph of the equation $y = a x ^ { 2 } + b x + c$ passes through the points $( 5 , - 104 ) , ( 5 , - 104 )$ , and $( 2 , - 26 )$ .

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An Introduction to Calculus: Limits, Derivatives, and Integrals

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Exam 7: Systems and Matrices

Graph the linear inequality. - y≤−3y \leq-3y≤−3