4.7 Identity and 4.7 Identity and Inverse MatricesInverse Matrices

What is an identity?

In math the identity is the number you multiply by to have equivalent numbers.

For multiplication it is one.

5 * 1 = 5, of course. How is this useful?

If you need to have a denominator of 40 in the fraction

8

3

40

15

5

5

8

3

What is an inverse?

The inverse is a number when multiplied by another number equals one.

136

36

4

9

9

4

14

4

4

1

1

4

4

14

The identity matrix is a square matrix with one down the diagonalsIn a 2 X 2 In a 3 X 3

10

01

100

010

001

Find the matrices that when multiply together are the identity matrix.

How do we find the inverse?

10

01

31

82

??

??

Find the inverse

Find the determinant of

6 – ( - 8) = 14

We will flip the diagonal of top left and bottom right, then change the signs the bottom left to top right diagonal.

31

82

21

83

31

82

Putting the part together

Take the determinant and put it under one and multiply it by the moved matrix.

21

83

14

1

Lets see if it works

10

01

140

014

14

1

6822

242486

14

1

31

82

21

83

14

1

Can there be matrices without inverses?

Yes, when the determinate equals zero.

Since a fraction can not have zero for a denominator. There would be no inverse.

0))12(12(32

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