1. Tell whether the matrix is equal to the fundraiser matrix. Explain.
Example 1
Compare Matrices
Tell whether the matrix is equal to the fundraiser matrix. Explain. = A 10 15 8 6 14 5 a. B 16 b. ( ) 2
The table shows the number of items sold during the first day of a class fundraiser. 1

2. Matrix B is not equal to the
Example 1
Compare Matrices
ANSWER = A 10 15 8 6 14 5 a. B 16 b. ( ) 2
The element is equal to 12. So, matrix A is equal to the fundraiser matrix because all corresponding
elements are equal. 6 ( ) 2
Matrix B is not equal to the
fundraiser matrix because the corresponding elements in the second row are not equal. 2

3. Tell whether the matrices are equal. Explain.
Checkpoint
Compare Matrices
Tell whether the matrices are equal. Explain. 2 2 1. , – 2 – 2
ANSWER
Equal; their dimensions are the same and the elements in corresponding positions are equal.

4. Tell whether the matrices are equal. Explain.
Checkpoint
Compare Matrices
Tell whether the matrices are equal. Explain. 1 – 1 1 ( ) 5 4 – , 2. 4 ( ) 1 3 – 2
ANSWER
Equal; their dimensions are the same and the elements in corresponding positions are equal.

5. [ ] Checkpoint Tell whether the matrices are equal. Explain. 1 3. 1 3
Compare Matrices
Tell whether the matrices are equal. Explain. 1 3. [ 1 3 ] , 3
ANSWER
Not equal; their dimensions are not the same.

6. Add or subtract, if possible. If not possible, state the reason.
Example 2
Add and Subtract Matrices
Add or subtract, if possible. If not possible, state the reason. a. 2 3 1 4 5 – + = 2 4 + 1 ( ) – 3 5 = 6 8 b. 4 5 1 – 2 3 = ( ) 2 – 4 1 5 3 = 3 2 – c. 3 12 11 – 2 1 15
It is not possible to subtract the matrices. They have different dimensions. = 6

7. Second Day of Fundraiser
Example 3
Use a Matrix Operation
The number of items sold during the second day of the class fundraiser is shown.
Second Day of Fundraiser
Extra Large
Large
T-shirts 12 5
Sweatshirts 4 3
Long sleeves 5 6 7

8. Add the matrix for the second day of the fundraiser to
Example 3
Use a Matrix Operation a.
Add the matrix for the second day of the fundraiser to
the matrix for the first day of the fundraiser.
First Day of Fundraiser
Extra Large
Large
T-shirts 10 15
Sweatshirts 8 12
Long sleeves 14 5 b.
What is the total number of large, long sleeve shirts
sold during the first two days of the fundraiser? 8

9. a. Add corresponding elements in the matrices.
Example 3
Use a Matrix Operation
SOLUTION
a. Add corresponding elements in the matrices. 10 = + 12 8 4 14 5 15 3 6 22 20 19 11
b. You need to find the element in the matrix from part (a) that corresponds to large, long sleeve shirts. The element in the third row and first column corresponds to large, long sleeve shirts. A total of 19 large, long sleeve shirts were sold. 9

10. Example 3 Extra Large Large T-shirts 22 20 Sweatshirts 12 15
Use a Matrix Operation
Extra Large
Large
T-shirts 22 20
Sweatshirts 12 15
Long sleeves 19 11 10

11. Add or subtract, if possible. If not possible, state the reason.
Checkpoint
Add and Subtract Matrices
Add or subtract, if possible. If not possible, state the reason. 3 1 3
ANSWER 4 3 6 4. + 2 4 – 2 2 3 7 4 5 6 + 2 – 5.
ANSWER
Not possible; their dimensions are not the same.

12. Add or subtract, if possible. If not possible, state the reason.
Checkpoint
Add and Subtract Matrices
Add or subtract, if possible. If not possible, state the reason. 5 2 4 3
ANSWER 1 2 – 6. – 3 1 2

13. Example 4 3 ( ) 3 1 – 2 = 2 1 – = 3 a. – 1 – 2 1 b. 4 3 2 1 – ( ) 4 3
Multiply a Matrix by a Scalar 3 ( ) 3 1 – 2 = 2 1 – = 3 a. – 1 – 2 1 b. 4 3 2 1 – ( ) 4 3 = 1 – 2 8 6 = 2 – 13

14. last month and this month are shown.
Example 5
Perform Multiple Operations
A store sells small and large steel DVD racks with wooden bases. Each size is available in three types of wood: walnut, pine, and cherry. Sales of the racks for
last month and this month are shown. 14

15. Example 5
Perform Multiple Operations
Use the matrices to find the average monthly sales for the two month period.
Last month ( ) A
This month ( ) B
Small
Large
Small
Large
Walnut 12 11
Walnut 14 15
Pine
Pine 28 20 36 28
Cherry 22 21
Cherry 20 17 15

16. Example 5
Perform Multiple Operations
SOLUTION
You can find the average monthly sales for the two month period by adding matrices A and B together and multiplying the sum by . 2 1 2 1 ( ) B + A = 12 11 28 20 22 21 14 15 36 17
Write the average. = 26 64 48 42 38 2 1
Add matrices A and B. 16

17. Example 5 13 13 = 32 24 21 19 Perform Multiple Operations
Multiply each element
by . 2 1 = 32 24 21 19 17

18. Solve the matrix equation for x.
Example 6
Solve a Matrix Equation
Solve the matrix equation for x. = 2x 3 1 – 4 15 + 12 6 2
SOLUTION
To solve the matrix equation, add the matrices on the left side of the equation, equate the element involving x with its corresponding element, and solve for x. = 2x 3 1 – 4 15 + 12 6 2
Write original equation. 18

19. Example 6
Solve a Matrix Equation 2x + 4 – 2 12 – 2
Add corresponding matrix
elements. = 6 15 6 15 2x 4 + =
Equate corresponding
elements and 12. 12 2x =
Subtract 4 from each side. 8 x =
Divide each side by 2. 4 19

20. Perform the indicated operation(s).
Checkpoint
Perform Matrix Operations and Solve Matrix
Equations
Perform the indicated operation(s). 1 – 2
ANSWER 10 4 – 2 6 7. 2 3 5 8. 7 2 – 3 1 + 5 4 35 5 25 15 –
ANSWER
Solve the matrix equation for x. x 25 9. 2 – + 24 5 10 = 27 30 12
ANSWER 3

21. Solve the matrix equation for x.
Checkpoint
Perform Matrix Operations and Solve Matrix
Equations
Solve the matrix equation for x. – 1 3 – 4 3 3
10. – =
ANSWER 8 3x 7 6 5 18 2