Warm-up 1.Review notes from Friday. 2.What is the dimension of the matrix below?

Warm-up1. Review notes from Friday.

2. What is the dimension of the matrix below?

1 25 10

29 1 18

Adding, Subtracting, and Scalar Multiplication of

Matrices

•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.

Examples

1.

2 0 4

3 10 12

3 2 2

4 6 0

15 2 4

6 7 1

6 6 4

12 8 8

9 5 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

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

Scalar Multiplication: each element in a matrix is multiplied by a constant.

1. 2 7 1 0 -14 2 0

2. 4 2 0

4 5

-8 0

16 -20

3. 5

1 2 3

4 5 6

7 8 9

-5 -10 15

-20 25 -30

35 -40 45

Examples.

More solving for a variable: A little more complex…

Upon first glance, these do not look equal. But if we manipulate them, we can see they are equal.

What pattern do you see? What can we do to get 5 to equal 25?How about 4 to equal 16?

Homework.Worksheet, problems 1-13.