Question 1

Use Gauss-Jordan row reduction to solve the system.

$\begin{aligned}
3 x + y - 2 z = & - 4 \
2 x - 3 y + 2 z = & 11 \
x + y + z = & 3
\end{aligned}$

Accepted Answer

A)  $( 1 , - 1,3 )$ 
B)  $\left( 9 , \frac { 2 } { 5 } , - 9 \right)$ 
C)  $\left( 0,9 , \frac { 2 } { 5 } \right)$ 
D)  $( 3,5 , - 5 )$ 
E)  inconsistent 
A)  $( 1 , - 1,3 )$ 
B)  $\left( 9 , \frac { 2 } { 5 } , - 9 \right)$ 
C)  $\left( 0,9 , \frac { 2 } { 5 } \right)$ 
D)  $( 3,5 , - 5 )$ 
E)  inconsistent

Question 2

Use Gauss-Jordan row reduction to solve the given system of equations.   $$\begin{array} { r } 
x + y + z + u + v = 13 \
y + z + u + v = 3 \
x + 2 y + 2 z + 2 u + 2 v = 16 \
x - y - z - z + 16 \
x - 2 y - 2 z - 2 u - 2 v = 4
\end{array}$$

Accepted Answer

A)  $( 8,4 - z - u - v , z , u , v )$ , z, u, v arbitrary 
B)    $( 9,3 - z - u - v , z , u , v )$ , z, u, v arbitrary 
C)  $( 10,3 - z - u - v , z , u , v )$ , z, u, v arbitrary 
D)  $( 6,3 - z - u - v , z , u , v )$ , z, u, v arbitrary 
E)  $( 13,4 - z - u - v , z , u , v )$ , z, u, v arbitrary 
A)  $( 8,4 - z - u - v , z , u , v )$ , z, u, v arbitrary 
B)    $( 9,3 - z - u - v , z , u , v )$ , z, u, v arbitrary 
C)  $( 10,3 - z - u - v , z , u , v )$ , z, u, v arbitrary 
D)  $( 6,3 - z - u - v , z , u , v )$ , z, u, v arbitrary 
E)  $( 13,4 - z - u - v , z , u , v )$ , z, u, v arbitrary

Question 3

Use Gauss-Jordan row reduction to solve the given system of equations.   $$\begin{array} { l } 
3 x - y - z = 4 \
x + y + z = 16
\end{array}$$

Accepted Answer

A)   $( 11 - z , 5 , z )$ , z arbitrary 
B)    $( 5,11 - z , z )$ , z arbitrary 
C)  $( 11,5,0 )$ 
D)  $( 5,10 - z , z )$ , z arbitrary 
E)  inconsistent 
A)   $( 11 - z , 5 , z )$ , z arbitrary 
B)    $( 5,11 - z , z )$ , z arbitrary 
C)  $( 11,5,0 )$ 
D)  $( 5,10 - z , z )$ , z arbitrary 
E)  inconsistent

Question 4

Find the intersection of the line through $( 0,1 )$ and $( 4.3,2 )$ and the line through $( 2.7,3 )$ and $( 5.8,0 )$ .  
If the equations of the system are redundant, or if a system is inconsistent, so indicate. Round your answer to the nearest tenth.

Accepted Answer

A)  $( 1.9,4 )$ 
B)  $( 3.8,1.9 )$ 
C)  $( - 9.0 , - 3.1 )$ 
D)  inconsistent 
E)  redundant 
A)  $( 1.9,4 )$ 
B)  $( 3.8,1.9 )$ 
C)  $( - 9.0 , - 3.1 )$ 
D)  inconsistent 
E)  redundant

Question 5

In November, 2003, the four organizations ranking 5 through 8 in home Internet users in the US were eBay, the U.S. Government, Amazon, and Lycos, with a combined audience of 111 million users. Taking  x to be the eBay audience in millions, y the U.S. Government audience in millions, z the Amazon audience in millions, and u the Lycos audience in millions, it was observed that  
 $\begin{array} { l } 
y - z = z - u \
x - y = 3 ( y - u ) + 4 \
x - y + z - u = 11
\end{array}$

How large was the audience of each of the four companies in November, 2003  (All amounts in millions.)

Accepted Answer

A) eBay: 35 
The U.S. Government: 25
Amazon: 25
Lycos: 24 
B)  eBay: 36
The U.S. Government: 26
Amazon: 25
Lycos: 24 
C)  eBay: 35
The U.S. Government: 26
Amazon: 25
Lycos: 23 
D)  eBay: 35
The U.S. Government: 26
Amazon: 24
Lycos: 24 
E)  eBay: 35
The U.S. Government: 26
Amazon: 25
Lycos: 24 
A) eBay: 35 
The U.S. Government: 25
Amazon: 25
Lycos: 24 
B)  eBay: 36
The U.S. Government: 26
Amazon: 25
Lycos: 24 
C)  eBay: 35
The U.S. Government: 26
Amazon: 25
Lycos: 23 
D)  eBay: 35
The U.S. Government: 26
Amazon: 24
Lycos: 24 
E)  eBay: 35
The U.S. Government: 26
Amazon: 25
Lycos: 24

Question 6

Use Gauss-Jordan reduction to solve the system of equations.  
$\begin{aligned}
2 x - 3 y & = 12 \
3 x - 5 y & = 12 \
x - y & = 12
\end{aligned}$

Accepted Answer

A)  $( 25,12 )$ 
B)  $( 22,36 )$ 
C)  $( 25,36 )$ 
D)  $( 22,12 )$ 
E)  $( 24,12 )$ 
A)  $( 25,12 )$ 
B)  $( 22,36 )$ 
C)  $( 25,36 )$ 
D)  $( 22,12 )$ 
E)  $( 24,12 )$

Question 7

You invested a total of $6,400 in three funds at the beginning of 2003, including an equal amount in PNF and CMBFX. You earned a total of $391 in interest for the year. How much did you invest in each of the three funds  Use the data given in the figure below. $$\begin{array} { | l | l | } 
\hline & \text { 2003 Yield } \
\hline \text { PNF (Pimco N. Y.) } & 6 \% \
\hline \text { CMBFX (Columbia Ore) } & 5 \% \
\hline \text { SFCOX } & 7 \% \
\hline
\end{array}$$  
PNF (Pimco N. Y.)
$__________
CMBFX (Columbia Ore)
$__________
SFCOX
$__________

Accepted Answer

$1,900; $1

Question 8

Find all solutions of the given system and choose the graph of the system that shows the solutions.

$\begin{array} { l } 
x - y = 12 \
x + y = 4
\end{array}$

Accepted Answer

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

Question 9

Use Gauss-Jordan row reduction to solve the system of equations.   $\begin{aligned}
1 x + 9 y + z & = 2 \
7 y + z & = 10
\end{aligned}$

Accepted Answer

A)  $( 1,2,0 )$ 
B)  $( 0,0,2 )$ 
C)  $( 0,0,3 )$ 
D)  Redundant 
E)  Inconsistent 
A)  $( 1,2,0 )$ 
B)  $( 0,0,2 )$ 
C)  $( 0,0,3 )$ 
D)  Redundant 
E)  Inconsistent

Question 10

The chart below shows the amount spent by three U.S. airlines to fly one available seat one mile in the fourth quarter of 2000. $\begin{array} { | l | l | l | l | } 
\hline \text { Airline } & \text { Continental } & \text { SkyWest } & \text { SouthWest } \
\hline \text { Cost } & 9.8 \text { cents } & 20.3 \text { cents } & 7.8 \text { cents } \
\hline
\end{array}$  
Suppose that, on a 2000-mile Miami-Memphis flight, Continental, SkyWest, and SouthWest flew a total of 170 empty seats, costing them a total of $48,520. If SkyWest had twice as many empty seats as SouthWest, how many empty seats did each of these three airlines carry on its flight

Accepted Answer

A) Continental: 50 
SkyWest: 70
SouthWest: 40 
B)  Continental: 50
SkyWest: 70
SouthWest: 50 
C)  Continental: 50
SkyWest: 80
SouthWest: 40 
D)  Continental: 60
SkyWest: 70
SouthWest: 50 
E)  Continental: 60
SkyWest: 80
SouthWest: 40 
A) Continental: 50 
SkyWest: 70
SouthWest: 40 
B)  Continental: 50
SkyWest: 70
SouthWest: 50 
C)  Continental: 50
SkyWest: 80
SouthWest: 40 
D)  Continental: 60
SkyWest: 70
SouthWest: 50 
E)  Continental: 60
SkyWest: 80
SouthWest: 40

Question 11

You own a hamburger franchise and are planning to shut down operations for the day, but you are left with 12 bread rolls, 17 defrosted beef patties, and 13 opened cheese slices. Rather than throw them out, you decide to use them to make burgers that you will sell at a discount. Plain burgers each require 1 beef patty and 1 bread roll, double cheeseburgers each require 2 beef patties, 1 bread roll, and 2 slices of cheese, and regular cheeseburgers each require 1 beef patty, 1 bread roll, and 1 slice of cheese. How many of each should you make  ?

Accepted Answer

A) Plain burgers: 4 Double cheeseburgers: 5
Regular cheeseburgers: 3 
B)  Plain burgers: 5
Double cheeseburgers: 3
Regular cheeseburgers: 4 
C)  Plain burgers: 5
Double cheeseburgers: 2
Regular cheeseburgers: 4 
D)  Plain burgers: 3
Double cheeseburgers: 6
Regular cheeseburgers: 2 
E)  ?Plain burgers: 6
Double cheeseburgers: 2
Regular cheeseburgers: 3 
A) Plain burgers: 4 Double cheeseburgers: 5
Regular cheeseburgers: 3 
B)  Plain burgers: 5
Double cheeseburgers: 3
Regular cheeseburgers: 4 
C)  Plain burgers: 5
Double cheeseburgers: 2
Regular cheeseburgers: 4 
D)  Plain burgers: 3
Double cheeseburgers: 6
Regular cheeseburgers: 2 
E)  ?Plain burgers: 6
Double cheeseburgers: 2
Regular cheeseburgers: 3

Question 12

Use Gauss-Jordan row reduction to solve the given system of equations.
​ $\begin{array} { l } 
x - 2 y + z - 4 w = 1 \
x + 3 y + 7 z + 2 w = 4 \
2 x + y + 8 z - 2 w = 5
\end{array}$

Accepted Answer

The answer of Use Gauss-Jordan row reduction to solve the...

Question 13

The chart below shows the amount spent by three U.S. airlines to fly one available seat one mile in the fourth quarter of 2000. $\begin{array} { | l | l | l | l | } 
\hline \text { Airline } & \text { United } & \text { American } & \text { SouthWest } \
\hline \text { Cost } & 11.3 \text { cents } & 11.0 \text { cents } & 7.8 \text { cents } \
\hline
\end{array}$   Suppose that, on a 3000-mile New York-Los Angeles flight, United, American and SouthWest flew a total of 190 empty seats, costing them a total of $60,900. If United had three times as many empty seats as American, how many empty seats did each of these three airlines carry on its flight

Accepted Answer

A) United: 130
American: 40
SouthWest: 30 
B)  United: 120
American: 30
SouthWest: 40 
C)  United: 30
American: 40
SouthWest: 120 
D)  United: 120
American: 40
SouthWest: 30 
E)  United: 120
American: 30
SouthWest: 30 
A) United: 130
American: 40
SouthWest: 30 
B)  United: 120
American: 30
SouthWest: 40 
C)  United: 30
American: 40
SouthWest: 120 
D)  United: 120
American: 40
SouthWest: 30 
E)  United: 120
American: 30
SouthWest: 30

Question 14

Use Gauss-Jordan row reduction to solve the given system of equations.   $$\begin{aligned}
x - y + z - u + v & = 0 \
y - z + u - v & = - 8 \
x - 2 v & = - 12 \
2 x - y + z - u - 3 v & = - 16 \
4 x - y + z - u - 7 v & = - 40
\end{aligned}$$

Accepted Answer

A)  $( - 6 , - 16 + z - u , z , u , 1 )$ , z, u arbitrary 
B)  $( - 9 , - 6 + z - u , z , u , - 8 )$ , z, u arbitrary 
C)  $( - 8 , - 6 + z - u , z , u , 2 )$ , z, u arbitrary 
D)  $( - 8 , - 9 + z - u , z , u , 1 )$ , z, u arbitrary 
E)  $( 2 , - 6 + z - u , z , u , - 8 )$ , z, u arbitrary 
A)  $( - 6 , - 16 + z - u , z , u , 1 )$ , z, u arbitrary 
B)  $( - 9 , - 6 + z - u , z , u , - 8 )$ , z, u arbitrary 
C)  $( - 8 , - 6 + z - u , z , u , 2 )$ , z, u arbitrary 
D)  $( - 8 , - 9 + z - u , z , u , 1 )$ , z, u arbitrary 
E)  $( 2 , - 6 + z - u , z , u , - 8 )$ , z, u arbitrary

Question 15

Conan the Great has boasted to his hordes of followers that many a notorious villain has fallen to his awesome sword: His total of 570 victims consists of evil sorcerers, warriors, and orcs. These he has slain with a total of 630 mighty thrusts of his sword--evil sorcerers and warriors each requiring 2 thrusts (to the chest) and orcs each requiring 1 thrust (to the neck).When asked about the number of warriors he has slain, he replies, "The number of warriors I, the mighty Conan, have slain is four times the number of evil sorcerers that have fallen to my sword!" How many of each type of villain has he slain  ?

Accepted Answer

A) Evil sorcerers: 23 Warriors: 48
Orcs: 488 
B)  Evil sorcerers: 12
Warriors: 48
Orcs: 510 
C)  Evil sorcerers: 48
Warriors: 12
Orcs: 510 
D)  Evil sorcerers: 12
Warriors: 37
Orcs: 488 
E)  Evil sorcerers: 12
Warriors: 48
Orcs: 488 
A) Evil sorcerers: 23 Warriors: 48
Orcs: 488 
B)  Evil sorcerers: 12
Warriors: 48
Orcs: 510 
C)  Evil sorcerers: 48
Warriors: 12
Orcs: 510 
D)  Evil sorcerers: 12
Warriors: 37
Orcs: 488 
E)  Evil sorcerers: 12
Warriors: 48
Orcs: 488

Question 16

In 2000, total revenues from sales of recorded rock, rap, and classical music amounted to $12.0 billion. Rock music brought in twice as much revenue as rap music and 600% the revenue of classical music. How much revenues were earned in each of the three categories of recorded music  ?

Accepted Answer

A) Revenues from sales of recorded rock: 7.2 Revenues from sales of recorded rap: 3.7
Revenues from sales of recorded classical music: 1.2 
B)  Revenues from sales of recorded rock: 7.2
Revenues from sales of recorded rap: 3.6
Revenues from sales of recorded classical music: 1.2 
C)  Revenues from sales of recorded rock: 1.2
Revenues from sales of recorded rap: 7.2
Revenues from sales of recorded classical music: 3.6 
D)  Revenues from sales of recorded rock: 7.1
Revenues from sales of recorded rap: 3.7
Revenues from sales of recorded classical music: 1.2 
E)  Revenues from sales of recorded rock: 3.6
Revenues from sales of recorded rap: 7.2
Revenues from sales of recorded classical music: 1.2 
A) Revenues from sales of recorded rock: 7.2 Revenues from sales of recorded rap: 3.7
Revenues from sales of recorded classical music: 1.2 
B)  Revenues from sales of recorded rock: 7.2
Revenues from sales of recorded rap: 3.6
Revenues from sales of recorded classical music: 1.2 
C)  Revenues from sales of recorded rock: 1.2
Revenues from sales of recorded rap: 7.2
Revenues from sales of recorded classical music: 3.6 
D)  Revenues from sales of recorded rock: 7.1
Revenues from sales of recorded rap: 3.7
Revenues from sales of recorded classical music: 1.2 
E)  Revenues from sales of recorded rock: 3.6
Revenues from sales of recorded rap: 7.2
Revenues from sales of recorded classical music: 1.2

Question 17

Find the solution to the system of equations.   $$\begin{array} { l } 
- x + \frac { 5 } { 2 } y = 3 \
- 2 x + 5 y = 6
\end{array}$$

Accepted Answer

A)  $\left( 2 , - \frac { 8 } { 5 } \right)$ 
B)  $( 0,4 )$ 
C)  $( - 10,0 )$ 
D)  An infinite number of solutions 
E)  No solutions 
A)  $\left( 2 , - \frac { 8 } { 5 } \right)$ 
B)  $( 0,4 )$ 
C)  $( - 10,0 )$ 
D)  An infinite number of solutions 
E)  No solutions

Question 18

Find all solutions of the given system, and check your answer graphically.

$\begin{aligned}
- 4 x + 5 y & = - 4 \
8 x & = 10 y + 2
\end{aligned}$

Accepted Answer

A)  $( 0,0 )$ 
B)  $\left( - \frac { 3 } { 10 } , \frac { 5 } { 8 } \right)$ 
C)  $\left( \frac { 5 } { 8 } , \frac { 3 } { 10 } \right)$ 
D)  redundant 
E)  inconsistent 
A)  $( 0,0 )$ 
B)  $\left( - \frac { 3 } { 10 } , \frac { 5 } { 8 } \right)$ 
C)  $\left( \frac { 5 } { 8 } , \frac { 3 } { 10 } \right)$ 
D)  redundant 
E)  inconsistent

Question 19

Given that the number of U.S. 10th graders who were alcohol-free was 50% more than the number who had used alcohol, find the missing data. $$\begin{array} { | l | l | l | l | } 
\hline & \text { Used Alcohol } & \text { Alcohol-Free } & \text { Totals } \
\hline \text { U.S. } & x & y & 13,750 \
\hline \text { Europe } & z & w & 95,300 \
\hline \text { Totals } & 63,450 & 45,600 & \
\hline
\end{array}$$

Accepted Answer

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

Question 20

Use Gauss-Jordan reduction to solve the system of equations.
​ $\begin{array} { l } 
2 x - 3 y = 3 \
3 x - 5 y = 3 \
x - y = 3
\end{array}$

Accepted Answer

The answer of Use Gauss-Jordan reduction to solve the system...

Use Gauss-Jordan row reduction to solve the system. 3x+y-2z= -4 2x-3y+2z= 11 x+y+z= 3

Use Gauss-Jordan row reduction to solve the given system of equations. x+y+z+u+v=13 y+z+u+v=3 x+2y+2z+2u+2v=16 x-y-z-z+16 x-2y-2z-2u-2v=4

Use Gauss-Jordan row reduction to solve the given system of equations. 3x-y-z=4 x+y+z=16

Find the intersection of the line through $( 0,1 )$ and $( 4.3,2 )$ and the line through $( 2.7,3 )$ and $( 5.8,0 )$ . If the equations of the system are redundant, or if a system is inconsistent, so indicate. Round your answer to the nearest tenth.

Use Gauss-Jordan reduction to solve the system of equations. 2x-3y =12 3x-5y =12 x-y =12

Find all solutions of the given system and choose the graph of the system that shows the solutions. x-y=12 x+y=4

Use Gauss-Jordan row reduction to solve the system of equations. 1x+9y+z =2 7y+z =10

Use Gauss-Jordan row reduction to solve the given system of equations. x-2y+z-4w=1 x+3y+7z+2w=4 2x+y+8z-2w=5

Use Gauss-Jordan row reduction to solve the given system of equations. x-y+z-u+v =0 y-z+u-v =-8 x-2v =-12 2x-y+z-u-3v =-16 4x-y+z-u-7v =-40

In 2000, total revenues from sales of recorded rock, rap, and classical music amounted to $12.0 billion. Rock music brought in twice as much revenue as rap music and 600% the revenue of classical music. How much revenues were earned in each of the three categories of recorded music ?

Find the solution to the system of equations. -x+y=3 -2x+5y=6

Find all solutions of the given system, and check your answer graphically. -4x+5y =-4 8x =10y+2

Given that the number of U.S. 10th graders who were alcohol-free was 50% more than the number who had used alcohol, find the missing data. Used Alcohol Alcohol-Free Totals U.S. x y 13,750 Europe z w 95,300 Totals 63,450 45,600

Use Gauss-Jordan reduction to solve the system of equations. 2x-3y=3 3x-5y=3 x-y=3

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Exam 4: Systems of Linear Equations and Matrices