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Test bank for linear algebra and its applications 5th edition by lay ibsn 9780134022697

Test bank for linear algebra and its applications 5th edition by lay i...

Course

Computatnl Linear Alg (MAS 3114)

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Students shared 7 documents in this course

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University of Florida

Academic year: 2022/2023

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MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Perform the matrix operation.

####### - 3 10 - B) A- 1 =

####### - 2 - 2 -

. Find 5A.

A) - 15 5 0 10

####### - 2 - 1 -

####### 2 -

C) - 15 5 0 2

D) 2 6 5 7 Answer: A

Let B = - 1 1 7 - 3. Find - 4B. A) 4 - 4 - 28 12 B) - 4 4 28 - 12 C) 4 1 7 - 3 D) - 3 - 1 5 - 5 Answer: A
Let C =

####### -

. Find (1/2) C.

A) 3

####### -

B) 6

####### 4 - 1 -

C) 3

####### - 1 - 3 -

D) 12

4 20 Answer: C

Let A = 3 3 2 4

and B = 0 4 - 1 6

. Find 4A + B.

A) 12 7 7 10

B) 12 16 7 22

C) 12 16 1 10

D) 12 28 4 40 Answer: B

Let C =

and D =

####### - 2 - 7 -

. Find C - 2D.

A) - 3 9 - 6

B) - 1 3 - 2

C) 3

D) 3

6 4 Answer: C

Let A = - 1 2 and B = 1 0. Find 3A + 4B. A) 1 6 B) 2 2 C) - 3 4 D) - 1 4 Answer: A
Let A =

2 - 4

2 - 5 3 5

and B =

9 - 8

6 - 6
7 - 4

. Find A + B.

A) - 7 4 4 10 - 4

B) 11 - 12 - 8 - 11 - 4 1

C) 11 - 12 8 - 5

4 - 1

D) 11 - 5

8 - 11
4 1 Answer: B

Test Bank for Linear Algebra and Its Applications 5th Edition by Lay IBSN 9780134022697

Full Download: downloadlink/product/test-bank-for-linear-algebra-and-its-applications-5th-edition-by-lay-ibsn-

Full all chapters instant download please go to Solutions Manual, Test Bank site: downloadlink

Let A = - 2 3
- 7 - 2

and B = 2 10 - 7 6

. Find A - B.

A) - 4 - 7 0 - 8

B) 0 7

14 8

C) 4 - 7

14 4

D) 0 - 7 0 - 8 Answer: A

Let A = - 3 2 3 - 5

and B = 0 0 0 0

. Find A + B.

A) 0 0 0 0

B) - 3 2 3 - 5

C) 3 - 2

D) Undefined

Answer: B

Find the matrix product AB, if it is defined.

####### - 1 - 3 - C) A- 1 =

2 2

, B = - 2 0 - 1 2

#######

A) 6 - 1 4 - 6

B) 2 0

C) - 1 6 - 6 4

D) 2 - 6

1 1 Answer: C

A = 0 - 3 4 3

, B = - 2 0 - 1 1

A) 0 6

B) - 3 3 - 5 - 11

C) 3 - 3

11 3

D) - 8 - 6 4 6 Answer: C

A = 3 - 2 3 0

, B = 0 - 2 4 6

A) 0 4 12 0

B) - 18 - 8 - 6 0

C) - 8 - 18 0 - 6

D) - 6 30 - 8 Answer: C

A = - 1 3 1 6

, B = 0 - 2 6 1 - 3 2

A) 3 6 - 7

20 0 18

B) 3 - 7 0 6 - 20 18

C) 0 - 6 18 1

18 12

D) AB is undefined.

Answer: B

A is 2 × 4, B is 2 × 4. A) AB is undefined, BA is undefined. B) AB is 2 × 4, BA is 4 × 2. C) AB is 4 × 2, BA is 2 × 4. D) AB is 2 × 2, BA is 4 × 4. Answer: A

Find the transpose of the matrix.

8 4

4 0
7 7 A) 8 - 4 - 7 4 0 7

B) 4 0 7 8 - 4 - 7

C) - 7 - 4 0 8 4

D) 4 8 0 - 4 7 - 7 Answer: A

7 4 7 4 0 - 7 0 - 7 A) 4 7 4 7

7 0 - 7 0

B) 7 0 4 - 7 7 0 4 - 7

C) 0 7

7 4 0 7
7 4

D) 0 - 7 0 - 7 7 4 7 4

Answer: B

Decide whether or not the matrices are inverses of each other.

5 3 3 2

and 2 - 3 - 3 A) No B) Yes Answer: B

10 1
- 1 0

and 0 1 - 1 10 A) No B) Yes Answer: A

- 2 4 - 4

and

1 2

1 4 1 2

1 4 A) Yes B) No Answer: B

- 5 1
- 7 1

and

1 2 -

1 2 7 2 -

5 2 A) No B) Yes Answer: B

6 - 5
- 3 5

and

1 3

1 3 1 5

2 5 A) No B) Yes Answer: B

9 4 4 4

and - 0 0. 0 - 0. A) Yes B) No Answer: B

9 - 2 7 - 2

and

0 0.

7 4 -

9 4 A) No B) Yes Answer: A

- 5 - 1 6 0

and

0 1 6

1 5 6 A) Yes B) No Answer: B

2 - 1 0

1 1 - 2 1 0 - 1

and

1 - 1 2

3 - 2 4
1 1 1 A) No B) Yes Answer: A

Find the inverse of the matrix, if it exists.

A = - 3 - 4 3 - 4 A)

1 6

18 - 16

B) - 1 6

1 6 1 8 -

1 8

C) - 1 8

1 8
1616

D) - 1 6

1 6

18 - 18

Answer: D

A = 0 - 5 6 3 A) 0 1 6

1 5

1 10

B) 1 10

1 6 1 5

C) - 1 5

1 10

1 6

D) 1 10

1 6

1 5

Answer: D

Solve the system by using the inverse of the coefficient matrix. 40) 6x 1 + 5x 2 = 13 5x1 + 3x2 = 5 A) (-2, 5) B) No solution C) (-2, - 5) D) (5, - 2) Answer: A

6x 1 + 3x 2 = 0 2x1 = - 6 A) (6, - 3) B) (-3, 6) C) No solution D) (-3, - 6) Answer: B
- 3x 1 - 2x 2 = 2 6x1 + 4x2 = 8

A) (-2, - 2) B) - 23 + 32 x2, x2 C) No solution D) (2, 8)

Answer: C

2x 1 + 6x 2 = 2 2x1 - x2 = - 5 A) (-1, 2) B) (2, - 1) C) (-2, 1) D) (1, - 2) Answer: C
2x 1 - 6x 2 = - 6 3x1 + 2x2 = 13 A) (-3, - 2) B) (-2, - 3) C) (3, 2) D) (2, 3) Answer: C
10x 1 - 4x 2 = - 6 6x1 - x2 = 2 A) (-4, - 1) B) (1, 4) C) (4, 1) D) (-1, - 4) Answer: B
2x 1 - 4x 2 = - 2 3x1 + 4x2 = - 23 A) (-2, 5) B) (2, 5) C) (-5, - 2) D) (5, 2) Answer: C
- 5x 1 + 3x 2 = 8
- 2x1 + 4x2 = 20 A) (2, 6) B) (-6, - 2) C) (-2, - 6) D) (6, 2) Answer: A

Find the inverse of the matrix A, if it exists.

Answer: B

D) A- 1 does not exist. - 5 - 48) A = -

10 - - A) A- 1 = - - 1 0 - - - 1 0 B) A- 1 does not exist. C) A- 1 = - 0 1 - - - D) A- 1 = - - 0 1 - - - -

1. A =

    - - 1 - 1 - A) A- 1 =
    - - 2 - 1 -
    - - 2 - 2 -
                      - - B) A- 1 =
                               - 4 - 1 -
                      - -
                            - C) A- 1 does not exist. D) A- 1 =
                         -
                         -
                                     -
                         -
                         -
                                  -
                                  -
                                        -
                                        -

1. A =

       - A) A- 1 =
             -
                -
                -
       -
             -
                -
                -
       -
       -
             -
             -
                -
                -
                      - - 3 10 - B) A- 1 =
                               - 2 -
                      - -
    - - 1 - 3 - C) A- 1 =
    - - 1 - 3 -
    - - 2 - 7 -

Determine whether the matrix is invertible.

2 9 1 14 A) No B) Yes Answer: B

9 5 - 9 4 2 - 4

3 0 3 A) No B) Yes Answer: A

Identify the indicated submatrix.

0 1 - 4 - 5 4 - 1 0 7 2 5 - 7 0

. Find A12.

A) 4 B) - 5 7

C) 1 D) 2 5 - 7

Answer: B

2 6 1

2 0 - 1 0 3 - 6 3 6 3

. Find A21.

B) - 2 C) 6 D) 3

Answer: D

Find the matrix product AB for the partitioned matrices.

4 0 1 2 - 1 - 3 5 3 7

, B =

2 0 8 5 1 6 2 2 4 - 1 0 3

A) - 4 - 1 32 23

17 - 3 14 - 1 21 11 46 52

B) - 8 0 32 20 - 5 - 6 14 8 - 7 18 46 C)

4 - 1 0 3
12 - 3 0 - 9 28 - 7 0 21

D) - 4 - 1 32 23

17 - 3 14 - 1 21 11 46 52 Answer: D

A = 0 I I F

, B = W X Y Z

A) Y Z W + YF X + ZF

B) X W + XF Z Y + ZF

C) 0 Z FY FZ

D) Y Z W + FY X + FZ Answer: D

Solve the equation Ax = b by using the LU factorization given for A.

3 - 1 2

6 4 - 5 9 5 6

, b =

A =

1 0 0

2 1 0 3 4 1

3 - 1 2 0 2 - 1 0 0 4

A) x =

7 15

B) x =

58 51

C) x =

38 32

D) x =

2
13 Answer: D

1 2 4 3

1 - 3 - 1 - 4 2 1 19 3 1 5 - 9 7

, b =

2 0 4 3

A =

1 0 0 0

1 1 0 0 2 3 1 0 1 - 3 - 2 1

1 2 4 3 0 - 1 3 - 1 0 0 2 0 0 0 0 1

A) x =

27 9 8

B) x =

18 89
13

C) x =

D) x =

6
3
5 Answer: D

Find an LU factorization of the matrix A.

A = 4 - 1
- 24 9

A) A = 1 0 - 6 1

4 - 1 0 3

B) A = 1 0 4 1

6 - 1 0 3 C) A = 1 0
6 1

4 1 0 - 3

D) A = 1 0 6 1

4 - 1 0 - 3 Answer: A

Find the 3 × 3 matrix that produces the described transformation, using homogeneous coordinates. 68) (x, y) → (x + 7, y + 4) A) 1 0 4 0 1 7 0 0 1

B) 1 0 7 0 1 4 0 0 0

C) 1 0 7 0 1 4 0 0 1

D) 7 0 0 0 4 0 0 0 1 Answer: C

Reflect through the x-axis A) 1 0 0 0 - 1 0 0 0 1

B) - 1 0 0 0 1 0 0 0 1

C) - 1 0 0 0 - 1 0 0 0 1

D) 1 0 0 0 1 0 0 0 1 Answer: A

Find the 3 × 3 matrix that produces the described composite 2D transformation, using homogeneous coordinates. 70) Rotate points through 45° and then scale the x-coordinate by 0 and the y-coordinate by 0. A) 0 2 0 2 0

0 2 0 2 0 0 0 1

B) 0 - 0 2 0 0 2 0 0 0 0 1 C) 0 - 0 0 0 0 0 0 0 1

D) 0 2 - 0 2 0 0 2 0 2 0 0 0 1 Answer: D

Translate by (8, 6), and then reflect through the line y = x. A) 0 1 8 1 0 6 0 0 1

B) 0 1 6 1 0 8 0 0 1

C) 0 6 1 8 0 0 0 0 1

D) - 1 0 - 8 0 - 1 - 6 0 0 1 Answer: B

Find the 4 × 4 matrix that produces the described transformation, using homogeneous coordinates. 72) Translation by the vector (4, - 6, - 3) A) 4 0 0 0 0 - 6 0 0 0 0 - 3 0 0 0 0 1

B) 1 0 0 4 0 1 0 - 6 0 0 1 - 3 0 0 0 1

C) 0 0 0 4 0 0 0 - 6 0 0 0 - 3 0 0 0 1

D) 1 0 0 - 4 0 1 0 6 0 0 1 3 0 0 0 1 Answer: B

Rotation about the y-axis through an angle of 60° A) 0 0 3 /2 0 0 1 0 0

3 /2 0 0 0 0 0 0 1

B) 1 0 0 0 0 0 3 /2 0 0 - 3 /2 0 0 0 0 0 1 C) 0 3 /2 0 0

3 /2 0 0 0 0 0 1 0 0 0 0 1

D) 3 /2 0 0 0 0 1 0 0

0 0 3 /2 0 0 0 0 1 Answer: A

Determine whether b is in the column space of A.

1 2 - 3 1 4 - 6

3 - 2 5

, b =

2
3 A) No B) Yes Answer: B

1 0 2 5 8 - 10
3 - 3

, b =

4 3 4 A) Yes B) No Answer: B

Find a basis for the null space of the matrix.

1 0 - 7 - 4 0 1 5 - 2 0 0 0 0

A) 7

5 1 0

4 2 0 1

B) - 7 5 1 0

4
2 0 1

C) 1 0 0

0 1 0

D) 1 0

0 1 5

2 Answer: A

1 0 - 4 0 - 4 0 1 2 0 2 0 0 0 1 1 0 0 0 0 0

A) 4

2 1 0 0

B) 1 0

0 1 2 0 2

C) 1 0 0 0

0 1 0 0

0 0 1 0

D) - 4 2 1 0 0

4 2 0
1 1 Answer: A

Determine the rank of the matrix.

1 - 2 2 - 3 2 - 4 7 - 2

3 6 - 6 9

A) 4 B) 1 C) 3 D) 2 Answer: D

1 0 - 4 0 4 0 1 - 3 0 4 0 0 0 1 1 0 0 0 0 0

A) 3 B) 4 C) 5 D) 2 Answer: A

Test Bank for Linear Algebra and Its Applications 5th Edition by Lay IBSN 9780134022697

Full Download: downloadlink/product/test-bank-for-linear-algebra-and-its-applications-5th-edition-by-lay-ibsn-

Full all chapters instant download please go to Solutions Manual, Test Bank site: downloadlink

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Test bank for linear algebra and its applications 5th edition by lay ibsn 9780134022697

Course: Computatnl Linear Alg (MAS 3114)

7 Documents

Students shared 7 documents in this course

University: University of Florida

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MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Perform the matrix operation.

Let A =

-3 1

0 2 . Find 5A.

-15 5

0 10

-15 1

0 2

-15 5

0 2

2 6

5 7

Answer:

Let B =

-1 1 7 -3

. Find -4B.

4 -4 -28 12

-4 4 28 -12

4 1 7 -3

-3 -1 5 -5

Answer:

Let C =

-2

. Find (1/2) C.

-2

-1

-4

Answer:

Let A =

3 3

2 4 and B =

0 4

-1 6 . Find 4A + B.

12 7

7 10

12 16

7 22

12 16

1 10

12 28

4 40

Answer:

Let C =

-3

and D =

-1

-2

. Find C - 2D.

-3

-6

-1

-2

-9

-6

Answer:

Let A =

-1 2

and B =

1 0

. Find 3A + 4B.

1 6

2 2

-3 4

-1 4

Answer:

Let A =

2-4

-2-5

3 5

and B =

9-8

-6-6

-7-4

. Find A + B.

-7 4

4 4

10 -4

11 -12

-8-11

-4 1

11 -12

8-5

-4-1

11 -5

-8-11

-4 1

Answer:

Test Bank for Linear Algebra and Its Applications 5th Edition by Lay IBSN 9780134022697

Full Download: http://downloadlink.org/product/test-bank-for-linear-algebra-and-its-applications-5th-edition-by-lay-ibsn-9780134022697/

Full all chapters instant download please go to Solutions Manual, Test Bank site: downloadlink.org