Which augmented matrix represents the following system of

equations?

1 2 3 4

0% 0%0%0%

1143

86

xy

yx

11

8

4

6

3

01.

11

8

4

6

3

12.

11

8

3

6

4

13.

11

8

3

6

4

04.

Which matrix represents the following system of equations?

1 2 3

0% 0%0%

4

3

y

x

41

311.

410

3012.

7113.

An ice skating rink does not list their prices. I paid £22.25 for 2 children and 3 adults. The group in front of

me paid £20.50 for 5 children and 1 adults. Which system of equations would allow us to determine the

prices for children and adults

1 2 3 4

0% 0%0%0%

1. 2x + 5y = 22.253x + y = 20.50

2. 2x + 3y = 22.255x + y = 20.50

3. 22.25x + 20.50y = 42.755x + 6y = 11

4. (22.25/2)x + (22.25/3)y = 0(20.50/5)x + (20.50)y = 0

What is the solution to the following system of equations?

2x + 2y = 4x – y = -6

1 2 3 4 5 6

0% 0% 0%0%0%0%

1. x=½ and y=-¼

2. x=2 and y=¼

3. x=-2 and y=4

4. x=2 and y=-4

5. There are an infinite number of solutions

6. There are no solutions

What is the solution to the following system of equations?

4x + 2y = 6-16x - 8y = 12

1 2 3 4 5 6

0% 0% 0%0%0%0%

1. x=3/2 and y=0

2. x=-1/2 and y=4

3. x=0 and y=3

4. x=3 and y=-3

5. There are an infinite number of solutions

6. There are no solutions

Which of the following matrices has an inverse?

1 2 3 4

0% 0%0%0%

21

631.

14

282.

21

973.

28

3124.

Which of the following matrices does not have an inverse?

1 2 3 4 5 6

0% 0% 0%0%0%0%

11

241.

28

142.

12

303.

43

874.

inverses havenot do

above theof one than More5.

inverses have All6.

Let A= . What is the value of A-1?

1 2 3 4

0% 0%0%0%

21

23

31

22

4

11.

21

23

4

12.

31

22

8

13.

21

23

8

14.

1 2 3 4

0% 0%0%0%

? is What .02

70 1

AALet

02

701.

07

202.

07

20

3.

07

12

10

4.

Calculate .

1 2 3 4

0% 0%0%0%

3

23

15

69

3151.

19108

36892.

827

11253.

827

11254.

Let A= and B= .What is the value of AB?

1 2 3 4

0% 0%0%0%

13

45

21

24

411

18241.

61

18142.

32

693.

618

1144.

Let A= and A-1= .Use this information to solve

3x+y=55x+2y=9

What is the value of x?

0% 0%0%0%

25

13

35

12

1. x=2

2. x=0

3. x=1

4. x=-3

If A is a 3x4 matrix and B is a 4x2 matrix, then what is the size of AB?

3x2

4x4

2x3

None

of the

se

0% 0%0%0%

1. 3x2

2. 4x4

3. 2x3

4. None of these

The point is transformed by the matrix . Which is its new position?

1 2 3 4

0% 0%0%0%

2

3

23

12

5

81.

49

262.

1

03.

01

414.

Let and . Calculate .

1 2 3

0% 0%0%

31

62A

511

42B AB

3862

11351.

1135

38622.

1511

2443.

Let A= and B= . Find the

element in row 2, column 1 of the product matrix AB.

131

623

142

32

21

14

Given two matrices A and B, what must be true about their sizes in order to calculate the matrix product AB?

1 2 3

0% 0%0%

1. A and B must have the same number of rows

2. A must have as many rows as B has columns

3. A must have as many columns as B has rows

If A= ,what is AT?

0% 0%0%0%

047

131

297

297

131

0471.

717

933

2102.

012

439

7173.

297

047

1314.

Let A= . Calculate tr(A).

683

714

302

Which of the following is an identity matrix?

1 2 3 4

0% 0%0%0%

01

101.

00

002.

11

113.

10

014.

Which of the following is a symmetric matrix?

1 2 3 4

0% 0%0%0%

278

734

8411.

12

212.

463

631

3123.

31

744.

Which of the following relations shows that matrix addition is

commutative?

A+B

=B+A

A+(

B+C)=(A

+B)+

C

k(A

+B)=kA

+kB

0% 0%0%

1. A+B=B+A

2. A+(B+C)=(A+B)+C

3. k(A+B)=kA+kB

Let and .

Calculate .

1 2 3

0% 0%0%

31

62A

511

42B

BA

217

501.

212

1002.

1511

2443.

The determinant of a matrix A and the determinant of its transpose AT

are not equal.

0% 0%0%

1. True

2. False

3. Don’t know

Calculate the determinant of .

42

13

The determinant of a 2x2 matrix is -7. What is the determinant of the

transpose of this matrix?

Which of the following statements is false?

1 2 3 4

0% 0%0%0%

1. If the determinant of a matrix is zero then the matrix has two identical rows.

2. If a square matrix has two identical rows then its determinant is zero.

3. Both are false.

4. Neither are false.

Which of the following is an upper triangular matrix?

1 2 3 4

0% 0%0%0%

300

750

8011.

138

031

0022.

800

020

0063.

600

408

0024.

Consider . If then this equation has infinitely many

solutions.

Tru

e

Fal

se

0%0%

bax 0a

1. True

2. False

What is the size of this matrix?

2 x

3 3

x 2 6

0% 0%0%

421

79

13

1. 2 x 3

2. 3 x 2

3. 6

If A and B are both 3x2 matrices then which of the following are not

defined?

A+B

ATB

AB

ABT

All

of thes

e a.

..

0% 0% 0%0%0%

1. A+B

2. ATB

3. AB

4. ABT

5. All of these are defined

Let A= and B= . If A and B are equal what is the value of ?

12

63

2

3