Adding and SubtractingMatrices

What is the size/dimension?

3410

200

318

67237

89511

36402

20

11 0759

6

0

7

9

Organize the following information about your CD collection

Writing a Matrix

Rap: 4 groups, 6 solo artists, 0 collectionsRock: 8 groups, 3 solo artists, and 3 collectionsR & B: 1 group, 5 solo artists, 2 collections

4 6 0

8 3 3

1 5 2

4 8

1

6 3

5

0 32

• Only matrices with the same dimensions can be added and subtracted.

• The resulting matrix has the same dimension of the two matrices being added or subtracted.

Remember

Tell whether the matrices can be added

3 3 44 5 6

3 3 4 9

4 5 6 8

+[ [] ]

2 33 4 6 7

3 4 1 8 4 3

[ [

[ [

] ]

] ]+

+

To add two matrices, they must have the same order. To add, you simply add corresponding entries.

34

03

12

70

43

35

)3(740

0433

13)2(5

44

40

23

Example

1.

2 0 4

3 10 12

3 2 2

4 6 0

15 2 4

6 7 1

2 4 0 6 4 0

3 15 10 2 12 4

3 6 2 7 2 1

Add the corresponding elements in each matrix

6 6 4

12 8 8

9 9 1

Be careful, there is a mistake here

Subtracting MatricesTo subtract two matrices, they must have the same order. You simply subtract corresponding entries.

232

451

704

831

605

429

2833)2(1

)4(65015

740249

603

1054

325

Try this

724

113

810

051

708

342

2. 3 4

0 2

4 6 8

0 2 4

We can’t add because they are different dimensions!!!

3. 2 18

20 5

4 2

5 1

2 ( 4) 18 2

20 ( 5) 5 1

6 20

25 6

4.

3 10 2

10 8 6

0 1 0

5 4 3

2 1 0

8 10 4

3 5 10 4 2 3

10 2 8 1 6 0

0 ( 8) 1 ( 10) 0 ( 4)

8 6 1

12 7 6

8 11 4

Questions?

Other resources:http://www.intmath.com/matrices-determinants/matrix-multiplication-flash.php

Assessment

Organizing Data

As we know, matrices are a useful way to organize and keep track of data.

For example if you have a business, it is important to keep track of revenue (income) and expenses (costs). You can find how much profit has been made by subtracting expenses from revenue.

Profit = Revenue – Expenses

If the profit is negative, did you make any money?

Finding a Profit Matrix• You own two stores that sell household appliances. The matrices on the board show revenue and expenses for three months at each store. You can find out how much profit has been made by subtracting expenses from revenue. If the profit is a negative number, you lost money!!

•Write a matrix that shows the monthly profit for each store.

•Which store had higher overall profits during the three-month period?

•What store lost money? In which month?

Closure Question

Two matrices are added. Their sum is a matrix with all zero entries. •What would need to be true about the matrices?

•What would need to be true about the corresponding entries of the matrices?

•Explain why matrices that are different sizes can not be added or subtracted?