Name______Date______Per_____PreAPAlgII
Unit 4 Matrices Review
Make sure you can do all of the following and understand the rules for multiplying, adding, subtracting, etc. for the always, sometimes, and never type questions.
Use the matrices above to evaluate. If not possible, explain why.
1) 2)
3) 4)
Olympic Medal SpecificationsGold / Silver / Bronze
Weight (lb) / 1.25 / 1.25 / 1
% copper / 7.5 / 7.5 / 90
Hours of handicrafting / 19.65 / 18.30 / 18.45
5) Use the table for a-d.
(a) Display the data in the form of a matrix, M.
(b) What are the dimensions of M?
(c) What is the value of the matrix entry with the address ? What does it represent?
(d) What is the address of the entry that shows the percent of copper in a bronze medal?
Find the determinant and the inverse for problems 6 and 7.
6) 7)
Evaluate using the matrices below for problems 9-12. If not possible, explain why.
8) EF9) FH
10) HG11)
12) The tables show the prices and number of tickets sold for three theater performances.
Adult / StudentThursday / $5 / $2.50
Friday / $7.50 / $4.25
Saturday / $9 / $5.75
Thursday / Friday / Saturday
Adult / 67 / 196 / 245
Student / 104 / 75 / 154
(a) Organize each table as a matrix.(b) Write the matrix product to find the amount of
money collected for each performance.
(c) Find the total collected for adult tickets and for student tickets for the three performances. Justify your answer with matrices and a complete sentence.
13) Find D=14) Find the inverse of
15) Verify that are inverses by hand.
Use Augmented Matrices to solve the following systems of equations.
16) 17)
18) A laboratory has one solution of 25% hydrochloric acid (HCl) and one solution of 12% HCl. A mixture requires 60 liters of 20% HCl. How many liters of each must be used?
(a) Write a system of linear equations to represent this situation. Identify your variables.
(b) Use Cramer’s Rule to solve for the number of liters needed. Justify your answer symbolically and with a complete sentence.
Write the matrix equation for the system. Solve using your choice of method.
19) 20)
21) In gymnastics,Team USA won 27 awards, which gave them 87 points. The team won three times as many 1st-place award as 2nd-place awards. Use the table to write a system of equations to represent this situation. Write the matrix equation for the system and solve it to determine how many of each type of award the team won.
Place / PointsFirst / 5
Second / 4
Third / 1
22.)Find the Determinant
- b.
23) At an end-of-season sale, a souvenir shop gave away small gifts values at $5 for sales of $25 to $74.99; medium gifts valued at $8 for sales of $75 to $149.99; and large gifts valued at $12.50 for sales above $150. The store gave away 102 gifts worth a total of $654 and six times as many small gifts as large gifts.
(a) Write a system of linear equations to represent this situation. Identify your variables.
(b) Use Cramer’s Rule to solve for the number of small, medium, and large gifts the shop gave away. Justify your answer symbolically and with a complete sentence.
24) Solve for x:
25) Find the value of x so that the matrix does not have an inverse:
26) Use Row Operations to solve each system of equations. Justify your answer algebraically .
- b.