Algebra 2

Today:• Class Announcements• Wednesday Warm-Up• 4.4 Notes• Begin Homework• Return 4.1-4.3 Quizzes

Wednesday Warm-UpTry both problems on your own…

Vocabulary: identity matrix, inverse matrix

4.4 – Identity and Inverse Matrices

Objectives:1. Find the identity matrices2. Find 2x2 inverse matrices3. Find an inverse matrix using a

calculator4. Use inverse matrices to solve

matrix equations

1. Find the identity matrices

5 + 0 = 5 because 0 is the additive identity

4 x 1 = 4 because 1 is the multiplicative identity

Therefore,

A x ? = A, ? will be the identity matrix.

Dependent on the dimensions of A.

If you need a 2x2 matrix

If you need a 3x3 matrix

10

01

100

010

001

2. Find 2x2 inverse matrices

5 + -5 = 0 because -5 is the additive inverse that gives the additive identity

2 x ½ = 1 because 1 is the multiplicative inverse that gives multiplicative identity

Therefore,

A x ? = I because ? is the inverse matrix that gives the identity matrix.

What is the inverse matrix?

2. Find 2x2 inverse matrices

The inverse of matrix:

Find the inverse of a square matrix:1. Find the determinant of A2. Switch the down and negate the

up

dc

baA

ac-

b-d

Adet1

A 1-

Determinant of A ≠ 0!

2. Find 2x2 inverse matrices

The inverse of matrix:

Find the inverse of a square matrix:1. Find the determinant of A2. Switch the down and negate the

up

42

23A

ac-

b-d

Adet1

A 1-

Determinant of A ≠ 0!

 

2. Find 2x2 inverse matrices

The inverse of matrix:

Find the inverse of a square matrix:1. Find the determinant of A2. Switch the down and negate the

up

24

13A

ac-

b-d

Adet1

A 1-

Determinant of A ≠ 0!

 

3. Find inverse matrices using a calculator

The inverse of matrix:

Find the inverse of a matrix:1. Input the matrix2. On main screen, type matrix

name with x-1 (inverse key)3. Convert to fractions if desired

24

13A

 

3. Find inverse matrices using a calculator

The inverse of matrix:

Find the inverse of a matrix:1. Input the matrix2. On main screen, type matrix

name with x-1 (inverse key)3. Convert to fractions if desired

42

23A

 

3. Find inverse matrices using a calculator

The inverse of matrix:

Find the inverse of a matrix:1. Input the matrix2. On main screen, type matrix

name with x-1 (inverse key)3. Convert to fractions if desired

3-31-

1-02

1-10

A

 

4. Use inverse matrices to solve matrix equations

Why use inverse matrices?

To solve equations!

AX = B, solve for the mystery matrix X

1 -2

4 -7X

7 2

-1 9

LNM

OQPLNM

OQP

X-51 4

-29 1LNM

OQP

4. Use inverse matrices to solve matrix equations

-3 4 0 2 3 10X +

5 -7 5 6 7 4

X-29 -48

-21 -34LNM

OQP

Why use inverse matrices?

To solve equations!

AX = B, solve for the mystery matrix X

4. Use inverse matrices to solve matrix equations

-1 2 1 0 -2 6

2 2 1 X 12 1 6

-4 4 -2 24 2 12

12

4 1 0

X 6 3

-8 -2 0

Why use inverse matrices?

To solve equations!

AX = B, solve for the mystery matrix X

Algebra 2

Homework:• pg. 227 #16, 18, 19, 25, 26, 29

• CHAPTER 4 TEST ON THURSDAY, NOVEMBER 8th!