5.8 HW Decide whether or not the matrices are inverses of ...

5.8 HW Name____________________________________________Period:____________

Decide whether or not the matrices are inverses of each

other.

1) 5 3 and 2 -3

32

-3 5

11

24

2)

-2 4 4 -4

and

1

1

24

11

33

3)

6 -5 -3 5

and

1

2

55

2 -1 0

1 -1 2

4) -1 1 -2 and -3 -2 4

1 0 -1

-1 1 1

1 -1 2

2 -1 0

5) -3 -2 4 and -1 1 -2

-1 1 1

1 0 -1

Find the inverse, if it exists, for the matrix. 6) -3 4 6 -4

7) 3 0 34

8) -3 -2 05

1 -1 3 9) 1 0 5

2 -1 8

1 3 2 10) 1 3 3

278

7 -5 2 11) 14 -9 4

7 -4 2

4 -2 0 3 12) 12 -4 0 6

6 -8 0 9 0 0 -6 0

5 -5 6 -2 13) 5 -4 -2 -1

10 -9 4 -3 0 -10 12 0

Solve the system by using the inverse of the coefficient matrix.

14) -5x + 3y = 8 3x - 6y = -30

15) 3x + 5y = -10 -3x - 6y = 9

16) 9x - 5y - z = 39 x + 7y + 2z = 56

3x + y + z = 33

17) -3x - y - 8z = -36 -6x - 7z = -34 5y + z = 9

18) 2x + 8y + 6z = 20 4x + 2y - 2z = -2 3x - y + z = 11

Use a graphing calculator to find the inverse of the matrix.

Give five decimal places, if necessary.

3 -4

19) A = 2 7

0.932

1.52 5.55 4 20) A = -0.63 7.33 3.21

8.2 0.003 -2.8

1

Use a graphing calculator and the method of matrix inverses to solve the system. Give five decimal places, if necessary.

21) x - 2y = 3.7 2.85x + y = -8.23

22) x + ey + 2z = 2 ex + y + 2z = 4 3x + ey + z = 6

Solve the problem. 23) A company makes 3 types of cable. Cable A requires 3 black, 3 white, and 2 red wires. B requires 1 black, 2 white, and 1 red. C requires 2 black, 1 white, and 2 red. The company used 100 black, 110 white and 85 red wires. How many of each type of cable were made?

24) A bakery sells three types of cakes, each requiring the amount of ingredients shown.

Cake I Cake II Cake III

flour 2

4

2

sugar 2

1

2

eggs 2

1

3

To fill its orders for these cakes, the bakery used 72 cups of flour, 48 cups of sugar, and 55 eggs. How many cakes of each type were made?

25) A bookstore is having a sale. All books included in the sale have a colored sticker on them to indicate the sale price. There are green stickers, red stickers, and orange stickers. Bob, Sue, and Fred each make purchases of books that are on sale. Each row of the table gives information about the numbers of book purchases and the total cost of the purchase (before taxes).

Person Green Red Orange Total Cost

Bob 1 2 2

$29.34

Sue 1 3 2

$36.21

Fred 1 2 3

$34.66

Use this information to set up a matrix equation of the form AX = B, which can be solved to determine the price for each type of sale book. Solve this matrix equation to find the price of a book with an orange sticker.

122 Use the fact that for A = 1 3 2 , A-1 =

123 5 -2 -2 -1 1 0 . -1 0 1

26) Matt bought 3 pounds of oranges and 2 pounds of apples and paid $4.14, before tax. Andy bought 4 pounds of oranges and 3 pounds of apples and paid $5.83, before tax. Use this information to set up a matrix equation of the form AX = B, which can be solved to determine the price per pound for oranges and apples. Solve this matrix equation to find the price per pound of oranges.

Use the fact that for A = 3 2 , 43

A-1 = 3 -2 . -4 3

2

Answer Key Testname: CA 5.8 HW

1) Yes 2) No 3) Yes 4) No 5) No 6)

11 33

11 24

7)

1 3

0

11 -4 4

8) 12

- 3 - 15

0

1 5

9) The inverse does not exist.

10)

-3 10 -3

2 -4 1

-1 1 0

11) The inverse does not exist.

12)

1 -2

1 4

0

0

3

3 -4

1 -2

0

0

0

0

1 -6

3

5 -6

1 -3

0

13) The inverse does not exist. 14) {(2, 6)} 15) {(-5, 1)} 16) {(8, 6, 3)} 17) {(1, 1, 4)} 18) {(2, -1, 4)} 19)

0.33803 1.45078 -0.10363 0.62821

20) 0.15171 -0.11491 0.08500

-0.18145 0.27379 0.05467 0.44411 -0.33622 -0.10815

21) {(-1.57817,-3.73223)} 22) {(-2.01284, 2.71182, 0.67317)} 23) 15 A; 25 B; 15 C 24) 13 Cake I; 8 Cake II; 7 Cake III 25) $5.32 26) $0.76 per pound

3

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