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Name: _______________________________
Period: _______ Date: _______________
REVIEW 4-1 to 4-5
State the dimensions of each matrix.
1.
é 0 -4 7 -2 ù
ê 8 5 6 2 ú
ê
ú
êë 4 -2 3 -5 úû
2.
[ -3 -3 7]
Solve each equation.
3. [ -2x 22 -3z ] = [ 6x -2y 45 ]
5.
é -5 3x + 1 ù
é -5 x - 1 ù
ê 2y - 1 3z - 2 ú = ê 3y 5z - 4 ú
ë
û
ë
û
4.
é 7x - 8 ù
é 20 ù
ê -3y + 6 ú = ê 2y + 3 ú
ë
û
ë
û
6.
é 2x + y ù
é 0 ù
ê 3x + 2y ú = ê -2 ú
ë
û
ë û
7. The table gives ticket prices for a concert. Write a 2 x 3 that represents the cost
of a ticket.
Cost Purchased in
Advance.
Cost Purchased at
the Door
Child
$6
Student
$12
Adult
$18
$8
$15
$22
Perform the indicated matrix operations. If the matrix does not exist, write
impossible.
8.
é 2 -1 8 ù
é -1 4 -3 ù
7ê
- 2 ê
ú
ú
ë 4 7 9 û
ë 7 2 -6 û
9.
3 é 8 12 ù 2 é 27 -9 ù
+ 4 êë -16 20 úû 3 êë 54 -18 úû
é1 ù
é 0 ù é10 ù
-2 ê ú + 4 ê ú - ê ú
ë2 û
ë 5 û ë18 û
10.
é 4 -1 0 ù
é -2 4 5 ù
ê -3 6 2 ú
ê
ú
û , B = ë 1 0 -9 û , and C =
Use A = ë
following.
11. -3b
12. -2b – 3c
é10 -8 6 ù
ê -6 -4 20 ú
ë
û
to find the
13. A + 0.5C
ECONOMICS. For Exercises 14 and 15, use the table that shows loans by an
economic development board to women and men starting new businesses.
1999
2000
2001
Women
Businesses Loan Amt ($)
27
$567,000
41
$902,000
35
$777,000
Businesses
36
32
28
Men
Loan Amt ($)
$864,000
$672,000
$562,000
14. Write two matrices that represent the number of new businesses and loan
amounts, one for women and one for men.
15. Find the sum of the numbers of new businesses and loan amounts for both men
and women over the three-year period expressed as a matrix.
Determine whether each matrix product is defined. If so, state the dimensions of the
product.
16 . A3x5 * B5x8
17. M3x2 * A3x2
18. P9x1 * Q1x9
Find each product, if possible. If it is not possible, write impossible.
é 3 -2 7 ù é 3 -2 7 ù
ê 6 0 -5 ú · ê 6 0 -5 ú
û ë
û
18. ë
é 1 ù
[ 4 0 2 ] · êê 3úú
êë -1 úû
20.
19.
é 1 ù
ê 3ú · 4 0 2
]
ê ú [
êë -1 úû
RENTALS. For exercises 21 – 23, use the following information.
For their one-week vacation, the Montoyas can rent a 2-bedroom condominium for
$1,796, a 3-bedroom condominium for $2,165, or a 4-bedroom condominium for
$2,538. The table shows the number of units in each of three complexes.
Sun Haven
Surfside
Seabreeze
2-Bedroom
36
29
18
3-Bedroom
24
32
22
4-Bedroom
22
42
18
21. Write a matrix that represents the number of each type of unit available at each
complex and a matrix that represents the weekly charge for each type of unit.
22. If all of the units in the three complexes are rented for the week at the rates
given the Montoyas, express the income of each of the three complexes as
a matrix.
23. What is the total income of all three complexes for the week?
Find the value of each determinant.
24.
4 1
-2 -5
25.
2 -1
3 -9.5
26.
0.5 -0.7
0.4 -0.3
Evaluate each determinant using expansion by minors.
27.
2 -4 1
2 7 -6
3 0 9
8 4 0
-1 5 7
28.
1 -1 3
Evaluate each determinant using diagonals.
29.
1 2 -4
2 1 3
1 4 -6
1 8 0 2 3 3
30.
0 5 -1
31. Find the area of a triangle whose vertices have coordinates (3, 5), (6, -5), and
(-4, 10).