11 12 13 14

21 22 23 24

31 32 33 34

mn mn mn mn

a a a a

a a a a

a a a a

a a a a

Row 1

Row 2

Row 3

Row m

Column 1 Column 2 Column 3 Column 4

A matrix of m rows and n columns is called a matrix with dimensions m x n.

2 3 41.) 1

12

3 8 9

2.) 2 5

6 7 8

103.)

7

4.) 3 4

2 X 33 X 3

2 X 11 X 2

3 5

11.) 4

40

3 02.)

0 3

1 2 3

3.) 0 1 8

0 0 1

4.) 2

55.)

6.) 3

3 X 2 2 X 2 3 X 3

1 X 2 2 X 1 1 X 1

To add matrices, we add the corresponding elements. They must have the same dimensions.

5 0 6 3

4 1 2 3A B

A + B5 6 0 3

4 2 1 3

1 3

6 4

2 1 3 0 0 02.)

1 0 1 0 0 0

2 1 3

1 0 1

When a zero matrix is added to another matrix of the same dimension, that same matrix is obtained.

To subtract matrices, we subtract the corresponding elements. The matrices must have the same dimensions.

1 2 1 1

3.) 2 0 1 3

3 1 2 3

1 1 2 ( 1)

2 1 0 3

3 2 1 3

0 3

3 3

5 4

4 1 6 51.)

6 3 7 3

1 3 2 2 1 52.)

4 0 5 6 4 3

2 6

13 0

1 4 7

2 4 8

ADDITIVE INVERSE OF A MATRIX:

1 0 2

3 1 5A

1 0 2

3 1 5A

Find the additive inverse:

2 1 5

6 4 3

2 1 5

6 4 3

Scalar Multiplication:

1 2 3

1 2 3

4 5 6

k

We multiply each # inside our matrix by k.

1 2 3

1 2 3

4 5 6

k k k

k k k

k k k

3 01.) 3

4 5

9 0

12 15

2

1 2

2.) 5 4 1

0 5

x

y

x

2

5 10 5

20 5 5

0 25 5

x

y

x

812

026

2

14

58

132

y

x

812

026

528

11432

y

x

812

026

56

0432

y

x

812

026

21012

086

y

xScalar Multiplication:

6x+8=26

6x=18

x=3

10-2y=8

-2y=-2

y=1

• Associative Property of Addition(A+B)+C = A+(B+C)

• Commutative Property of AdditionA+B = B+A

• Distributive Property of Addition and Subtraction S(A+B) = SA+SB

S(A-B) = SA-SB• NOTE: Multiplication is not included!!!