### Chapter 4 Jeopardy

```Alg 2 - Chapter 4 Jeopardy
Matrix
Operations
Multiplying
Matrices
Determinants, Area
of Triangle &
Cramer's Rule
Identity and
Inverse Matrices
Solving Systems
Using Inverse
Matrices
10
10
10
10
10
20
20
20
20
20
30
30
30
30
30
40
40
40
40
40
50
50
50
50
50
10 points
1 2 
The matrix 3 4  has
5 6 
1 2 
The matrix 3 4  has
5 6 
1 2 1
-3 1   2

 
5

0 
20 points
Perform the indicated operation.
1 2 1 5
-3 1   2 0  

 

Perform the indicated operation.
2+5 
1 2 1 5 1  1


-3 1   2 0  -3+2 1+0

 
 

2
 
-1
7

1
30 points
Perform the indicated operation.
4
-9

2  2


5  4
8


8
Perform the indicated operation.
4
-9

2  2



5  4
- 6
2


-13 - 3 
8  4 - 2



8 -9 - 4
2-8 

5 -8
40 points
Solve the matrix equation for x and y.
0
2x 0  4
 4 -4y   4 -20

 

Solve the matrix equation for x and y.
 2x 0   4 0 
 4 -4y    4 -20 

 

2x  4
-4y = -20
2
2
x  2
-4
-4
y  5
50 points
Solve the matrix equation for x and y.
-3 4 -5 1 7 -16 
2x 





-11 5 4 2 -4y -20
Solve the matrix equation for x and y.
-3 4  -5 1 7 -16 
2x 





-11
5
4
2
-4y
-20

 
 

2 x(3)  (5)  7
2(2)(11)  4  -4 y
6 x  5  7
44  4  4 y
5 5
48  -4 y
6 x 12

6 6
x  2
-4
-4
-12  y
10 points
20 points
Perform the indicated operation.
1
-4

2  4


3 0
1


-1
Perform the indicated operation.
1
-4

2  4


3 0
1

-1
1(4)  2(0)

 4(4)  3(0)
1(1)+2(-1) 

-4(1)+3(-1) 
1+(-2)   4 -1 
 4+0

 


-16+0 -4+(-3)  -16 -7 
30 points
Perform the indicated operation.
4
 -3 2 -5   
 4 -6 3  1  

 0 
 
Perform the indicated operation.
4
-3 2 -5  
 4 -6 3  1 

 
0 
 3(4)  2(1)  ( 5)(0) 


 4(4)  (6)(1)  3(0) 
 12  2  0 



16  (6)  0 
 10 
 10 


40 points
Perform the indicated operation.
Perform the indicated operation.
 2 -4 0   1 2  3 -1 
0 3 6   -3 0   0 2  


 

-1 5 1   5 1   4 5 
 2 -4 0    4 1  


 0 3 6   -3 2  
-1 5 1   9 6  
2(1)  4( 2)  0(6) 
 2(4)  4(3)  0(9)
  0(4)  3( 3)  6(9)
0(1)  3( 2)  6( 6) 
 1(4)  5(3)  1(9)
 1(1)  5( 2)  1(6) 
2  (8)  0 
8  12  0
 0  (9)  54
0  6  36  
 4  (15)  9
-1  10  6 
 20 -6 
 45 42 


-10 15
50 points
Perform the indicated operation.
Perform the indicated operation.
3
1
 -1 3 
1

2

6
2 

  33
2

1

 
2

3


2 
2
1 -3  
 4

3
1
 -1 3 

2

1
18


2 


 2

1


2
 3 -9  

3

2 
2

 4

1
 3

2
-3   0
21  


17
4   5 -  

2 

1(0)  3(5)

 3 (0)  4(5)
 2

0  (15)

0  20

17 
)
2 

3
17 
( 21)  4(  )
2
2 
1( 21)  3( 
51 
2

63
 ( 34) 
2

21 

-15

 20

93 
2

5
2 
10 points
NO CALCULATOR!
NO CALCULATOR!
det  6(4)  3(0)
 24  0  24
20 points
NO CALCULATOR!
Evaluate the determinant of the matrix.
2
1

-3

-4 
NO CALCULATOR!
Evaluate the determinant of the matrix.
2
1

-3

-4 
 2(4)  1(3)  8  3  5
30 points
NO CALCULATOR!
Evaluate the determinant of the matrix.
1
-3

 2
2
3
1
1

-1
0 
NO CALCULATOR!
Evaluate the determinant of the matrix.
40 points
NO CALCULATOR!
Find the area of the triangle with the given vertices.
NO CALCULATOR!
Find the area of the triangle with the given vertices.
5 2 1
1
Area=  0 0 1
2
3 -3 1
50 points
You MAY use a CALCULATOR!
Use Cramer's rule to solve the linear system.
Show what you are entering in your calculator.
3x  5 y  8
4 x  7 z  18
yz 3
You MAY use a CALCULATOR!
Use Cramer's rule to solve the linear system.
Show what you are entering in your calculator.
3
5
0
4
0
7  41
0
1
1
8
5
0
18 0 7
3 1 1 41
x

1
41
41
3
4
0
8
3x  5 y  8
4 x  7 z  18
yz 3
0
18 7
3 1 41
y

1
41
41
z
3
5
8
4
0
0 18
1 3
-82

2
41
41
10 points
Write the identity 3x3 matrix
Write the identity 3x3 matrix
1 0 0 
0 1 0 


0 0 1 
20 points
NO CALCULATOR!
5 -2 
1 5 -2  1 5 -2 
A 

 





3 2 -7 3  15  14 -7 3  1 -7 3 
7 5
1
1
5 -2 
 

-7 3 
30 points
NO CALCULATOR!
Find the inverse of the matrix. SHOW WORK!
2
1

4

3
NO CALCULATOR!
Find the inverse of the matrix. SHOW WORK!
2
1

4

3
1
1
A 
2
1
1 3
 
2 -1
3
4 -1
3
-4 
1 3



2  6  4 -1
3
-4   2
 

2  1
 2

-2 

1

-4 

2
40 points
NO CALCULATOR!
Find the inverse of the matrix. SHOW WORK!
6
7

-2

-2
NO CALCULATOR!
Find the inverse of the matrix. SHOW WORK!
6
7

-2 

-2 
1
1
A 
6
7
-2 +2
-2 +2
1





-2 -7 6  12  (14) -7 6 
-2
-1 1
1 -2 +2  

 

7

2 -7 6  - 3
 2 
50 points
NO CALCULATOR!
Find the inverse of the matrix. SHOW WORK!
4
2

-3

-5
NO CALCULATOR!
Find the inverse of the matrix. SHOW WORK!
4
2

-3
-5
1
1
A 
4
2
-5 +3
-5 +3
1





-3 -2 4  20  (6) -2 4 
-5
1 -5 +3




14 -2 4 
3
5
14 - 14 


2
1
 7
7 
10 points
You MAY use a CALCULATOR!
Solve the matrix equation. Show what you are
3
1

2
x


1
1
-3

0
1
2

4
You MAY use a CALCULATOR!
Solve the matrix equation.Show what you are entering in your calculator.
3
1

2
1 0
x 

1
-3 1
1 -2 
1
A 

-1
3


1 -2  3 2
1
-1 3 1 1  x  -1




2

4
-2  1


3 -3
 7 -2 -6
x

-10 3 10 
0
1
2

4
20 points
You MAY use a CALCULATOR!
Use an inverse matrix to solve the linear system.
3x – 7y = -16
-2x + 4y = 8
You MAY use a CALCULATOR!
Use an inverse matrix to solve the linear system
3x – 7y = -16
 3 -7   x 
-16 
-2x + 4y = 8

    
-2
4  y
 8
7

-2

2
1
A 

-1 - 3 

2 
7
7


-2 - 2   3 -7   x  -2 - 2  -16 



 



-1 - 3  -2 4   y  -1 - 3   8 


2 
2 
 x  4
 y   4
   
30 points
You MAY use a CALCULATOR!
Use an inverse matrix to solve the linear system.
2x + 3y = -8
x + 2y = -3
You MAY use a CALCULATOR!
Use an inverse matrix to solve the linear system.
2x + 3y = -8
x + 2y = -3
2
1

3  x 




2   y
 2 -3
1
A 

-1
2


 2 -3  2
-1 2 1


-8
-3
 
3  x   2 -3 -8




2   y  -1 2 -3
 x  -7 
 y   2
   
40 points
Skating Party - Your planning a birthday party
for your younger brother at a skating rink. The
per child, and there is a limit of 20 people. You
have \$50 to spend. Use an inverse matrix to
determine how many adults and how many
children you can invite.
Skating Party - Your planning a birthday party for your younger brother at a skating
rink. The cost of admission is \$3.50 per adult and \$2.25 per child, and there is a limit of
20 people. You have \$50 to spend. Use an inverse matrix to determine how many
adults and how many children you can invite.
3.50 2.25  a 
50 
  
1



1  c 

 20
9 
4
5
5 
1
A 

14 
- 4
 5
5 
9 
4
4
5
5  3.50 2.25  a   5






14  1
1  c   4
- 4
 5
 5
5 
a   4 
c   16 
   
-
9 
5  50 

14   20 
5 
50 points
Stock Investment – You have \$9000 to invest in
three Internet companies listed on the stock
market. You expect the annual returns for
companies A, B, and C to be 10%, 9%, and 6%,
respectively. You want the combined investment
in companies B and C to be twice that of
company A. How much should you invest in each
company to obtain an average return of 8%?
Stock Investment – You have \$9000 to invest in three Internet companies listed on the stock market. You expect
the annual returns for companies A, B, and C to be 10%, 9%, and 6%, respectively. You want the combined
investment in companies B and C to be twice that of company A. How much should you invest in each company
to obtain an average return of 8%?
A  B  C  9000
.1A  .09 B  .06C  .08(9000) rewrite: .1A  .09 B  .06C  720
B  C  2A
1
1
.1 .09

-2 1
1
.06 
1 
1
3

22
1
A  
 9

 28
 9
1
3

  22
 9

 28
 9
rewrite: -2 A  B  C  0
0
100
3
100
3
 A
B  
 
C 
0
100
3
100
3
9000 
 720 


 0 
1
- 
3

4
9

1
9 
1
- 
3 1
1

4
.1 .09
9 
 -2 1
1
9 
1

1   A  3
22
.06   B    
 9
1  C  
 28
 9
 A  3000 
 B    2000 
  

C   4000 
0
100
3
100
3
1
- 
3 9000 

4
720 

9
  0 
1
9 
Answer: You should invest \$3000 in company A, \$2000 in company B, and \$4000 in company C
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