Inverse Matrices - Kuta Software

Kuta Software - Infinite Algebra 2

Name___________________________________

Inverse Matrices

Date________________ Period____

For each matrix state if an inverse exists. 1)

−9 −2

−9 −2

2)

−2 −6

1 1

3)

4 −9

−5 6

4)

0 −6

0 4

Find the inverse of each matrix. 5)

11 2

−5 −1

6)

0 −1

−2 −9

7)

−1 −1

7 7

8)

1 −6

−1 −3

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Worksheet by Kuta Software LLC

9)

3 −4

11)

−9 −5

13)

2 −11

15)

−2 −9

−2 6

−6 −4

−10 8

2 8

10)

−6 −4

11 7

12)

5 6

14)

−2 6

−2 8

16)

−3 8

3 7

−8 −9

Critical thinking questions: 17) Give an example of a 2×2 matrix with no inverse.

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18) Give an example of a matrix which is its own inverse (that is, where A −1 = A)

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Worksheet by Kuta Software LLC

Kuta Software - Infinite Algebra 2

Name___________________________________

Inverse Matrices

Date________________ Period____

For each matrix state if an inverse exists. 1)

−9 −2

−9 −2

2)

No

3)

4 −9

−2 −6

1 1

Yes

−5 6

4)

Yes

0 −6

0 4

No

Find the inverse of each matrix. 5)

11 2 1 2

7)

−1 −1

−5 −1

6)

−5 −11

7 7

−2 −9

9 2 1 − 2

8)

No inverse exists

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0 −1

1 −6 1 3 2 − 3

-1-

−1 0

−1 −3 1 9 1 − 9 −

Worksheet by Kuta Software LLC

9)

11)

3 −4

−2 6

10)

3 5 2 5

1 5 3 10

−9 −5

−6 −4

2 3 5 6

−

13)

12)

−

4 47 11 − 94

3 2

14)

5 47 1 − 47

2 8

4 9 2

−1

11 2 −3

−

−8 −9

−2

−

−2 −9

5 6

11 7

−3

−10 8

−

15)

7 2 2

1

2 −11

−6 −4

8 3 5 3

−2 6

−2 8

−2

−

1 2 1 2

3 2

16)

−3 8 7 45 8 45

−

−1

3 7 1 15 1 15

Critical thinking questions: 17) Give an example of a 2×2 matrix with no inverse. Many answers. Ex:

1 2

18) Give an example of a matrix which is its own inverse (that is, where A −1 = A)

2 4

Many answers. Ex:

−10 −11

9 10

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Worksheet by Kuta Software LLC