Matrices: Simplifying Algebraic Expressions

Combining Like Terms & Distributive Property

Matrix

Rectangular arrangement of numbers into rows and columns.

65

43

Matrix

Row: horizontal arrangement of numbers

Column: vertical arrangement of numbers

This matrix has 3 rows

and two columns.

k

n

m

v

y

x

10

9

4

6

5

3

Matrix Vocabulary

The plural form of matrix is matrices.

The numbers in a matrix are called elements or entries.

A matrix that has the same number of rows as columns is called a square matrix.

Dimension of a matrix

Dimension is determined by:

Row x Column

This matrix has a dimension of 2 x 3 or 2 by 3.

z

y

b

a

y

x

10

8

4

3

5

6

Operations with Matrices

To add or subtract matrices, matrices must have the same dimensions.

To add or subtract matrices, add or subtract corresponding entries to form one matrix.

Corresponding entries have the same row number and the same column number.

Operations with Matrices

Examples:

1. [A] + [B] 2. [A] – [B] 3. [B] – [A]

0

20

25

15A

15

6

25

10B

Operations with Matrices

Example:

4. [C] + [D] 5. [C] – [D]

n

m

j

h

y

xC

15

5

10

7

5

3

n

m

j

h

y

xD

8

5

21

11

6

8

Scalar Multiplication

Scalar Multiplication: multiplication of a matrix by a real number.

To multiply a matrix by a scalar, multiply each entry by the real number to form a new matrix.

Real numbers are sometimes called scalars.

Scalar Multiplication

Example:

6. 9[E] 7. –3[F]

)5(

)35(

)42(

)2(

m

y

n

xE

)6(

)32(

)42(

)6(

m

y

k

wF

Let’s Practice!

Complete page 28, problems 38-41.Complete page 35, problems 56-58.Complete page 43, problems 90-95.

NO CALCULATOR!