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**Refer to the graph. **

**K**

**F**

**J**

1.

2.

Write hexagon GFEKJH as a matrix.

What are the dimensions of your matrix?

**E**

**G H**

**The matrix below shows the subscription figures for The Metropolitan Sentinel for a five-year period. **

1990

1991

1992

1993

1994

14 , 662

15 , 325

15

15

17

,

,

418

790

, 156

12 , 004

11

12 , 388

13

13

,

,

,

867

056

540

3.

4.

What is the subscription figure for the suburbs in

1993?

What does the entry in row 2 column 1 represent?

**Let A = **

7

2

2

6 0

2

and let B =

5

0

4

2

1

8

8

6

2

5.

6.

7.

What are the dimensions of the product AB?

What are the dimensions of the product BA?

Compute (if possible) each product.

**Use the following for 8 – 9. **

0

3

2

0

* x*

1

4

*3 y*

12

2 6

12

8.

9.

Solve for x

Solve for y

**Let A = **

3

6

1

10.

4

0

2

, B =

2

3

1

Calculate 2A – 5B

1

5

4

**, C = **

1

3 1

2

** and D = **

5

0

1

2

11.

** . **

Calculate 4C + D

**Solve each linear system graphically. **

**Sketch a picture for each problem, list the solution. **

**Determine whether the system is consistent and independent, inconsistent, or consistent and dependent. **

12.

*2 x x*

*4 y y*

2

12

13.

3

*3 x x*

2

*16 y*

7

*6 y*

*Solve each system of equations by substitution. Show work for all problems. If the system is inconsistent, write no solution. *

14.

*14 x x*

5

*2 y y*

10

11

15.

*4 x x*

6

*3 y y*

0

9

**Solve each system of equations by addition (or subtraction). Show work for all problems. If the system is inconsistent, write no solution. **

16.

5

*4 x x*

6

*3 y y*

6

27

17.

5

*2 x x*

* y*

*2 y*

5

13

**Solve using any method. **

18.

4

*3 x x*

5

*7 y y*

19

18

19.

3

*5 x x*

8

*6 y y*

22

3

0

21.

**Write a system of equations for the following problem. Solve using any method. **

**(To earn full credit for these problems, you must show the system of equations used and the work done to solve the system) **

20. The local cable television company offers two deals. Basic cable service with one movie channel costs $35 per month. Basic service with two movie channels costs $45 per month. Find the charge for the basic cable service and the charge for each movie channel.

Nathan’s monthly electric bill includes a fixed service charge and an additional charge for the number of kilowatt- hours (kWh) of electricity used. One bill, including a charge of 595 kWh of electricity, is $61.72. Another bill, including a charge for 650 kWh, is $67.11. Find the fixed charge and the cost per kilowatt-hour.

**Writing. **

22. Describe the graph of a following types of solutions in the coordinate plane.

A. One solution

B. No Solutions

C. Infinitely many solutions

23.

24.

Describe the graph of a following types of solutions in the coordinate space.

A.

B.

C.

One solution

No Solutions

Infinitely many solutions

When solving by substitution or addition/subtraction method, how do you know that you have:

A.

B.

One solution

No Solutions

C. Infinitely many solutions

**Graph the points in coordinate space. **

25. (5, -3, 2) 26. (-4, 2, -1)

**Graph the equations in coordinate space. **

26. 4x - 3y + 6z = -12 27. 9x + y - 3z = 9

**Solve using any method. **

28.

*2 x*

* y x*

2

* y*

*3 z*

* z*

* z*

2

7

12

30.

5

*2 x x x*

7

*4 y y y*

17

9

*3 z z z*

4

28

17

29.

3

*2 x x*

* x*

4

* y y*

8

* y*

6

2

* z z*

3

36

20