6. use matrices to represent and manipulate data, e.g., to represent payoffs or incidence...

Addition

Augmented Matrix

Element

Equation

Matrix Multiplication

Scalar Multiplication

Variable Matrix

Zero Matrix

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

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

Lab,in class, with a partner (one), finish in class- do at end. Do as much as you can.

You and your partner many turn in one paper, both names. Textbook p. 181 #1-6; need to learn how to use calculator with

matrices.

At home: textbook page: 172 #27 all parts, due next class