Download Algebra 2 Unit 2 Matrix Study Guide

Algebra 2 Unit 2 Matrix Study Guide
1. Determine the value of x in the following system of equations.
2. What ordered triple is the solution to this system?
3. What is the value of y in the solution to this system of equations?
4. If A is a 4 x 2 matrix, B is a 4 x 4 matrix, and C is a 2 x 4 matrix, what are the dimensions of A x C x
B?
5. A used clothing store sells shirts for $1.50 each, shorts for $2.00 each, and jeans for $3.00 each.
On Friday, they sold 45 shirts, 33 shorts, and 15 jeans. What matrix operation would compute
the total income for that day?
6. Evaluate
7. What is the inverse of
.
8. Determine the sum of
, if it exists.
9. Three friends went shopping at their favorite store. All the pants, shirts, and sweaters were on
sale, and articles of each type cost the same. The table shows the friends’ purchases.
Clothing Purchases and Costs
Betty
Wilma
Judy
# of pants
6
7
3
# of shirts
6
4
5
# of sweaters
3
0
3
Using the information in the table, determine the cost of each sweater.
Total Cost
$402.00
$283.00
$300.00
10. What is AB?
A=
11. Find the inverse of
,
B=
.
12. Ricardo has investments in Funds X, Y, and Z. Each fund invests money in both stocks and
bonds. The matrices show the dollar amounts invested in each fund and the annual yields. Use
this information to determine how many dollars Fund Y will earn in one year.
Fund X
Fund Y
Fund Z
Stocks
10000
20000
5000
Bonds
10000
15000
30000
Stocks
Bonds
Annual Yields
.05
.08
13. Evaluate
14. Matrix A represents the amount of fruit (O=Oranges; P=Pears; S=Strawberries), in pounds, Janice
purchased on three different trips to a store. Matrix B gives the price per pound of each type of
fruit.
B=
What matrix gives the amount Janice spent on each trip?
15. Abby, Kerry, and John designed three games, a, b, and c. They have sold some games and want
to expand their business by advertising on the Internet. This matrix gives their sales for the first
month.
Their goal is to double the number of games sold each month for the next 4 months. What
matrix represents their goal?
16. Among the matrices
matrix, and what is the inverse?
, one has an inverse. Which
17. Consider the given matrices:
A) What matrix, G, would be added to H to obtain J? Show your work algebraically.
B) What is H * K, if it can be computed. If the expression cannot be computed, explain why not.
C) What is K * J, if it can be computed. If the expression cannot be computed, explain why not.
18)
Cara’s teacher lists these 2 matrices as class examples. The teacher says that one of these
matrices has an inverse and one does not.
A) What is the determinant of each matrix? Show your algebraic work.
B) Cara says that J has an inverse but K does not. Do you agree with Cara? Why or why not?
C) Find the inverse of the matrix that has an inverse.
18.