View
239
Download
0
Category
Tags:
Preview:
Citation preview
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?
Recommended