# Matrices and Systems of Equations ### (Matrices and Systems of Equations)

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

### Suburbs

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