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