Worksheet A6: Adding Matrices/Scalar Multiplication

Use the matrices below to answer questions 1-13

, , ,

Part I: Give the dimensions of each matrix

1) D ______2) E ______3) F ______4) G ______

Part II: Find the indicated matrix, if possible.

5. –F 6. D + G 7. 3E

8. D – E 9. E – D 10. 2F + G

11. -2G 12. F – G 13. 2D + 3E
Matrix M below represents the number of gold, silver, and bronze medals won by athletes from the United States, Germany, and Russia in the 1996 Summer Olympic Games. Each ROW represents a different type of medal, and each COLUMN represents a different country.

14. What are the dimensions of matrix M? ______

15. Find the total number of medals won by the United States. ______

16. Find the total number of gold medals won by all three nations. ______

17. Describe the data in location m23 (row 2, column 3).

18. In the 1996 Summer Olympic Games, Athletes from China won 16 gold medals, 22 silver medals,

and 12 bronze medals. Write a new Matrix, A, that includes medals for all four countries.

(adapted from Holt, Rinehart and Winston’s Algebra 2 Textbook)

Worksheet B6: Matrix Multiplication

Directions: Perform the following matrix multiplications. If the operation is not possible, write “not possible.”

1. 2.

3. 4.

5. 6. 7.

Worksheet C6: 2 x 2 Determinants

Evaluate the following determinants.

1. / 2. / 3.
4. / 5. / 6.
7. / 8. / 9.

Worksheet D6: Determinants & Inverses

Evaluate the following determinants.

1. / 2.
3. / 4.
5. / 6.


Find the inverse of each matrix. If it does not exist, write “No inverse exists.”

7. / 8.
9. / 10.
11. / 12.

Worksheet E6: Solving Systems using Inverses of Matrices

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

1. / 2.
3. / 4.
5. / 6.
7. / 8.


Worksheet F6: Solving Systems Using Cramer’s Rule

Directions: Use Cramer’s rule to find the solution set for each of the following systems. If the equations are dependent, simply indicate that there infinitely many solutions.

1.
2.
3.
4.
5.
6.


Name ______Date______

Worksheet G6: Test Review!

Directions: Perform the following matrix operations by hand, then check with a graphing calculator.

1. 2.

3. 4.

5. Find if

6. 7. Find if .


8. Solve the system below using Cramer’s Rule. Show all steps!

9.  Check your answer to #8 by solving the system on the graphing calculator using inverses. Hint: use the formula

10.  Find the determinants of the following matrices by hand.

a) b) c)

11.  Multiply the matrices below by hand.

a) b)


12. Solve the system below by hand using inverses. Hint: use

12.  List all of the topics that you need to be able to do on the graphing calculator.

13.  List all of the topics that you need to be able to do by hand.

14.  For each question 12 and 13, put a smile next to the topic you find the easiest, and a frown next to the topic you find most difficult.