What is a matrix? How is it read? What is the dimension?

What is scalar multiplication? How is it done?

What are four properties of matrices?

• MATRIX: A rectangular arrangement of numbers in rows and columns.

• The ORDER of a matrix is the number of the rows and columns.

• The ENTRIES are the numbers in the matrix.

502

126rows

columns

This order of this matrix is a 2 x 3.

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

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

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!!!

What is a matrix? How is it read? What is the dimension?

A matrix is a rectangular arrangement of numbers in rows and columns. It is read by the rows and columns and the dimension tells the number of rows by columns.

What is scalar multiplication? How is it done?Scalar multiplication is the “distributive law” for matrices.What are four properties of matrices?Associative for addition, commutative for addition,

distributive for addition, and distributive for subtraction.

p. 203, 12-36 even, 37-41