Finite MATH

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1

Show all steps leading to your answers , including any intermediate results obtained using a graphing utility. Answers with minimal, unorganized, or no work will be marked incorrect. Circle your answer

Only analytical solutions will be accepted.

1. Find the inverse matrix A- 1 of the matrix A analytically. Do not use calculator.

Show all steps.

2. Check yourself using the rule

A- 1 × A = I2 where I2 =

3.

Show that the matrix does not have an inverse.

4. Solve the system using matrices.

5x + 3y = 16

7x + 4y = 22

5. Solve the system using matrices.

5x + 3y = 3

7x + 4y = 4

6. Solve the system using matrices.

4x + 3y = 4

2x + 5y = 2

7. Solve the following system using Gaussian elimination.

4x + 3y - 2z = 10

x - y + 3z = 6

x –2y + z = 0

8. Pivot the matrix about the first entry in the first row.

9. Pivot the matrix about the second entry in the first row.

10. Pivot the matrix about the first entry in the second row.

11. Pivot the matrix about the second entry in the second row.

12. Determine all solutions of the system.

x - 3y + z = 5

-2x + 7y - 6z = - 9

2x – 4y - 6z = 12

13. Determine all solutions of the system.

x - 2y + z = 1

-x + 2y - z = 2

-2x + 4y - 4z = 1

14. Add two matrices.

15. Subtract two matrices.

- =

16. Multiply the following matrices.

ú

û

ù

ê

ë

é

1

0

0

1

ú

û

ù

ê

ë

é

=

3

1

9

3

A

ú

û

ù

ê

ë

é

-

1

2

3

15

6

3

ú

û

ù

ê

ë

é

-

1

2

3

15

6

3

ú

û

ù

ê

ë

é

-

-

+

ú

û

ù

ê

ë

é

-

-

1

5

2

1

1

4

3

2

ú

û

ù

ê

ë

é

-

-

2

4

3

3

ú

û

ù

ê

ë

é

-

-

1

1

3

2

=

ú

ú

ú

û

ù

ê

ê

ê

ë

é

-

-

´

ú

û

ù

ê

ë

é

-

-

2

1

2

3

1

2

2

1

3

1

2

2

ú

û

ù

ê

ë

é

=

2

3

1

3

A