Matrix OperationsSection 3.5

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When could you use matrices?

A. Reading Data Charts

B. Solving Systems5 2 2 44

3 3 4 27

2 4 5 2 48

4 5 6 4 23

x y z w

x y z w

x y z w

x y z w

Definitions

A. Matrix is a rectangular arrangement of numbers into rows and columns1. Dimensions read row x column2. Address is read through location

B. Rows are numbers which are acrossC. Columns are numbers which are up

and downD. Scalar is a real number that

multiplies each entry

Identify the matrix of the following:

Example 11 2 3

4 5 6

1 2 3

4 5 6

2 3

Identify the matrix of the following:

Your Turn 16.781 16.29 17.318

1 3

Adding and Subtracting MatricesA. Add them like integers and correspond to the

same entryB. Must have same number of rows and

columns

Example 2

Solve 3 1 4 9

4 8 2 9

3+4 1 9

4 2 8 9

7 8

6 1

Example 3

Solve2 0 5

3 1 4

7

6

Your Turn

Solve4 0 6 2 3 5

1 5 3 4 1 8

1 7

5 9

Example 4

Solve 51 2

10

Example 5

Given the following below, solve for B – A

2 9 1

4 1 5

4 7 2 2 2 3 1 4

5 1 1 1 0 4 2 3A B C

B A2 2 3 4 7 2

1 0 4 5 1 1

Your Turn

Given the following below, solve for A – B

2 9 1

4 1 5

4 7 2 2 2 3 1 4

5 1 1 1 0 4 2 3A B C

Your Turn

1 10

6 47

Given the following below, solve for 2A – 3C 4 2 4 1 5 3 2

6 3 83 10 3 2 8 0 9

A B C D

Multiply by Scalar

2 4 6x

8 12x

Just like distribution property

Example 6

8 12

2 0

Solve4 6

21 0

Your Turn

1 10

6 47

Given the following below, solve for 2A – 3C 4 2 4 1 5 3 2

6 3 83 10 3 2 8 0 9

A B C D

Solve

Example 7

6

2

1 3 1 18

4 5 2 5

x

y

3 18x 6x

2 4y 2y

Solve

Example 8

52

1

8 3 9 13 42

5 6 10 4 0 16

x

y

Given,

Your Turn

3.2

.25

2 0 6.4 0

0.5 0.75 0.5 3

x

y

Assignment

Pg 1915-27 odd, 30A, 30B