Sec 8.1 – Matrices Review Voting methods & Matrix Applications Name:

Use the following matrices for the problems 1 - 13. Show ALL WORK by HAND and check with the calculator.

5723

A

3725

B

621123

C

233402

D 5 30 7 1

xE

y

1. 2. TD

3. EC = 4. CD =

5. AB 32 = 6. DC =

7. B D = 8. B E =

What are the dimensions of Matrix D?

Use the following matrices for the problems 1 - 13. Show ALL WORK by HAND and check with the calculator.

5723

A

3725

B

621123

C

233402

D 5 30 7 1

xE

y

9. C22 + D31 – B21 = 10. 2A

11. TD D

12. Create a 2x2, 3x3, and 5x 5 IDENTITY matrices

13. Are Matrices A and B inverses? Demonstrate how you can tell.

14. 2 2 22 1 6

ab

14.

4 1 6 6 272 3 2 8

ab c

15. The determinant of

3524

by hand and show work. 14. Find the determinant of

641320153

by hand and show work.

15. Find the inverse of

3524

by hand and show work. 16. Find the inverse of

2436

by hand and show work.

17. On one weekend, the Goxfield Theater reported the following ticket sales for three first-run movies, as shown in the matrix at the right. If the ticket prices were $6 for each adult and $4 for each child, what were the weekend sales for each movie?

Determine possible values for a, b, and c that would make the following matrix statement true.

Determine possible values for a and b that would make the following matrix statement true.

a = b = c =

a = b =