alg 2 - chapter 4 jeopardy matrix operations multiplying matrices determinants, area of triangle...
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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
10 points - Answer1 2
The matrix 3 4 has
5 6
20 points
Perform the indicated operation.
1 2 1 5
-3 1 2 0
1 2 1 5
-3 1 2 0
20 points - Answer
Perform the indicated operation.1 1 2+51 2 1 5
-3 -3+2
2
1 2 1+0
7
-1 1
0
30 points
Perform the indicated operation.
4 2 2 8
-9 5 4 8
30 points - Answer
Perform the indicated operation.
4 - 2 2 -4 2 2 8
-9
8
-9 - 4 5 -8 5 4
2 - 6
8
-13 -3
40 points
Solve the matrix equation for x and y.
2x 0 4 0
4 -4y 4 -20
40 points - Answer
Solve the matrix equation for x and y.
-4y =
2x
2 4
2 2
0 4 0
4 -4y 4 -20
-20
-4 -4
2 5
x
x y
50 points
-3 4 -5 1 7 -162
-11 5 4 2 -4y -20x
Solve the matrix equation for x and y.
50 points - Answer
2 (2 ( 3) ( 5)
-3 4 -5 1 7 -162
-11 5 4 2 -4y -20
11) 4 -4
44 4 4
6
7 ( 2)
6 5 7
5 5
6
48
-4
y
y
y
x
x
x
x
12
2
-4
-4
-12
6
yx
Solve the matrix equation for x and y.
10 points
10 points - Answer
20 points
Perform the indicated operation.
1 2 4 1
-4 3 0 -1
20 points - Answer
Perform the indicated operation.
-4 3
( ) ( ) ( )+ ( )
4( ) 3( )
1 2
1 2 1 2
4+0 1+(-2)
-1
4
0
4 0
4
6+0
1
-1
1 -1
1 -1
4 -1
-1
-4(
-4+(-3)
)+3( )
6 -
0
7
30 points
Perform the indicated operation.4
-3 2 -51
4 -6 30
30 points - Answer
Perform the indicated operation.
4 -6 3
( ) ( ) ( )
-3 2 -5
3 2 5
10
1
( )
4( ) ( 6)( ) 3( )
12 2 0
16 ( 6
4
1
0
4 1 0
4 1 0
0) 0
40 points
Perform the indicated operation.
40 points - AnswerPerform the indicated operation.
3 -1
0 2
4
0 3
2 -4 0
-1 5 1
1 2
-3
-1 5 1
5
4
-3
0
5 1
6
0 3
2 -4
1
0
2
6
9 6
( ) ( ) ( ) ( ) ( ) ( )
0( ) 3( ) 6( ) 0( ) 3( ) 6( )
( )
4 3 9
4 3 9
4 3 9( ) ( ) ( ) ( ) ( )
8 12 0 2 ( 8) 0
0 ( 9) 54
1 5 1 1 5 1
0 6 36
2 4 0 2 41 2 6
1
4
6
1 6
0
2
2
(
20 -6
15) 9
45 42
-10 - 1 1 0 156
50 points
Perform the indicated operation.
50 points - AnswerPerform the indicated operation.
1 3 -
2 2
1 3
2 33
24
1 182
3 3 -9
-1 3
3
2
1 6
31
-2 2
1
-3
1 2
2
-1
2
3
1 2
2
-3
4
4
3 34 4
2
0
5
0 5
0
1 3 1 3
93-15
25
20
21
17 -
2
( ) ( ) ( ) ( )
( ) ( ) ( ) ( )
510 ( 15) 21
263
0 20 ( 34
1721
217
21
2
25
)
2
-
2
10 points
NO CALCULATOR!
d
et
6(4)
3(0
0 2
)
424
10 points - Answer
NO CALCULATOR!
20 points
Evaluate the determinant of the matrix.
NO CALCULATOR!
2 -3
1 -4
20 points - Answer
Evaluate the determinant of the matrix.NO CALCULATOR!
2
-4
-3
1
1( 3
8) ) 52( 34
30 points
Evaluate the determinant of the matrix.
NO CALCULATOR!
1 2 1
-3 3 -1
2 1 0
30 points - Answer
Evaluate the determinant of the matrix.NO CALCULATOR!
40 points
Find the area of the triangle with the given vertices.
NO CALCULATOR!
40 points - Answer
Find the area of the triangle with the given vertices.NO CALCULATOR!
5 2 11
Area= 0 0 12
3 -3 1
50 points
Use Cramer's rule to solve the linear system. Show what you are entering in your calculator.
4
3 5
3
8
7 18x
x y
y
z
z
You MAY use a CALCULATOR!
50 points - Answer
Use Cramer's rule to solve the linear system. Show what you are entering in your
calculator.
4
3 5
3
8
7 18x
x y
y
z
z
You MAY use a CALCULATOR!
41
41 41
4 0 7
0 7 4 7 4 0
3 5 0
5 0 3
0 1 1
1 1 0
8
1 0
8 8
18 18 18
3 31
0 3
41 4
5
1
1 41 41
yx z
-82
41 41
1
2 3
1: ( , )1 2,Answer
10 points
Write the identity 3x3 matrix
10 points - Answer
Write the identity 3x3 matrix
1 0 0
0 1 0
0 0 1
20 points
NO CALCULATOR!
20 points - Answer
1 2 2 21 1 13 2 7 7 7 15 14 1
7
5 5 5
- -
5
-
- 3 3 3
5 -2
-7
- -
3
A
30 points
Find the inverse of the matrix. SHOW WORK!
NO CALCULATOR!
2 4
1 3
30 points - AnswerFind the inverse of the matrix. SHOW WORK!
NO CALCULATOR!
1
4
1
4
2
- -41 12 4 1 1
3
3 3
2 2
3 -2
21
-
3
6 4
1 3
- -
- 41
1
1
- 2 2
2
A
40 points
Find the inverse of the matrix. SHOW WORK!
NO CALCULATOR!
6 -2
7 -2
40 points - Answer
Find the inverse of the matrix. SHOW WORK!NO CALCULATOR!
1
-2
7
2 21 16 -2 7 7 12 ( 14)
7 -2
21
+ +
- -
+
7
6
-2
-2 -2
6 6
-1 1-2
7 6 - 3
22 -
A
50 points
Find the inverse of the matrix. SHOW WORK!
NO CALCULATOR!
4 -3
2 -5
50 points - Answer
Find the inverse of the matrix. SHOW WORK!NO CALCULATOR!
1
-3
2
3 31 14 -3 2 2 20 ( 6)
2 -5
+ +
- -
+
-
31
2
4
-5
-5 -
5 3 -
14 141 2
5
4
-7
-5
4
7
4
14
A
10 points
Solve the matrix equation. Show what you are entering in your calculator.
You MAY use a CALCULATOR!
3 2 1 0 2
1 1 -3 1 4x
10 points - Answer
Solve the matrix equation.Show what you are entering in your calculator.You MAY use a CALCULATOR!
1 1 -2
-1 3
1 -2 1 -2
-1 3
3 2 1 0 2
1 1 -3 1 4
3 2 1 0 2
1 1 -3 1 -1
3 4
x
A
x
7 -2 -6
-10 3 10x
20 points
Use an inverse matrix to solve the linear system.
3x – 7y = -16 -2x + 4y = 8
You MAY use a CALCULATOR!
20 points - Answer
Use an inverse matrix to solve the linear system3x – 7y = -16-2x + 4y = 8
1
7-2 -
23
-1 -2
7 7-2 - -2 -
2 23 3
-1 - -1 -2
3 -7 -16
-2 4 8
3 -7 -16
-2 4 8
2
A
x
y
x
y
4
4
Answer:
(4, )
4
x
y
You MAY use a CALCULATOR!
30 points
Use an inverse matrix to solve the linear system.
2x + 3y = -8 x + 2y = -3
You MAY use a CALCULATOR!
30 points - Answer
Use an inverse matrix to solve the linear system. 2x + 3y = -8 x + 2y = -3
You MAY use a CALCULATOR!
1
2 3 -8
1 2 -3
2 3 -8
1 2
-7
2 -3
-1 2
2 -3 2 -3
-1 2 -1 -
2
2 3
x
y
x
y
x
y
A
Answer: (-7, 2)
40 points
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.
40 points - AnswerSkating 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.
1
4 9 -
5 54 14
- 5 5
4 9 4 9 - -
5 5 5 54 14 4 14
- - 5 5
3.50 2.25 50
1 1 20
3.50 2.25
1 1
5 5
a
c
a
c
A
4
16
Answer: 4 a
dults and 16 children can attend the party
2
50
0
a
c
50 pointsStock 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%?
50 points - AnswerStock 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%?
rewrite: 720
rewrite - 2
-
.1 .09 .06 .08(9000)
:
.1 .09 .06
.1 .09
2 0
9000
1 1
.0
2 1
1
6
1
A
B C
B C A
A B C
A
B
C
A
A B
C
C
B
1
720
1 1 0 -
3 322 100 4
9 3 9
28 100 1 - -
9 3 9
1 1 0 -
3 322 100 4
900
9 3 9
28 100 1 - -
9 3 9
0
0
A
1 1 0
1 1 -
3 322 100 4
.1 .09 .06 7209 3 9
28 100
-2 1 1
1 9
1 - -
9 3
0
00
0
9
A
B
C
3000
2000
4000
Answer: You should in
vest $3000 in company A, $2000 in company B, and
$40
00
in comp
a
A
B
C
ny C
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