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Ch.7 Matrices Exam Questions 5th Edition

College Algebra, 5e (Young)

Chapter 7 Matrices

7.2 Matrix Algebra

1) Calculate A + B if A = [table ( ( -10 -9 -4 )( 2 8 9 ) )] and B = [table ( ( -8 7 -4 )( 10 1 6 ) )] .

A) [table ( ( 12 9 15 )( -18 -2 -8 ) )]

B) [table ( ( -18 -2 -8 )( 12 9 15 ) )]

C) [table ( ( -8 -2 -18 )( 15 9 12 ) )]

Diff: 2 Var: 1

Chapter/Section: Ch 07, Sec 02

Learning Objective: Add and subtract matrices.

2) Calculate AB if A = [table ( ( -2 10 -5 )( 3 8 -1 ) )] and B = [table ( ( 8 -8 )( -10 3 )( -10 10 ) )] .

A) [table ( ( -66 -4 )( -46 -10 ) )]

B) [table ( ( -10 -46 )( -4 -66 ) )]

C) [table ( ( -4 -66 )( -10 -46 ) )]

D) [table ( ( -46 -10 )( -66 -4 ) )]

Diff: 3 Var: 1

Chapter/Section: Ch 07, Sec 02

Learning Objective: Multiply two matrices.

3) Calculate 3B - 2A if A = [table ( ( -14 8 9 )( 19 8 -6 ) )] and B = [table ( ( 16 12 -17 )( 6 12 18 ) )] .

A) [table ( ( 45 10 -54 )( -74 0 61 ) )]

B) [table ( ( -74 0 61 )( 45 10 -54 ) )]

C) [table ( ( -20 20 66 )( 76 20 -69 ) )]

D) [table ( ( 76 20 -69 )( -20 20 66 ) )]

Diff: 2 Var: 1

Chapter/Section: Ch 07, Sec 02

Learning Objective: Add and subtract matrices.; Perform scalar multiplication.

4) Calculate D(A + B) if A = , B = [table ( ( 4 8 -10 )( 7 10 -10 ) )] and D = [table ( ( -8 -4 )( -6 -10 ) )] .

A) [table ( ( 32 -68 0 )( 18 -160 -6 ) )]

B) [table ( ( 54 -160 60 )( 44 -64 24 ) )]

C) [table ( ( 44 -64 24 )( 54 -160 60 ) )]

D) [table ( ( 32 -68 )( 18 -160 ) )]

Diff: 3 Var: 1

Chapter/Section: Ch 07, Sec 02

Learning Objective: Add and subtract matrices.; Multiply two matrices.

5) Calculate AB if A = [table ( ( 4 -4 )( -8 -3 )( 4 8 ) )] and B = [table ( ( -7 10 )( 3 -8 ) )] .

Diff: 3 Var: 1

Chapter/Section: Ch 07, Sec 02

Learning Objective: Multiply two matrices.

6) Solve for the indicated variables.

[table ( ( 4x - 4y -7 )( 6x - 10y -4 ) )] = [table ( ( -60 z )( -110 -4 ) )]

A) x = 5, y = -10, z = -7

B) x = -10, y = 5, z = -7

C) x = -10, y = -5, z = -4

D) x = 10, y = 5, z = -7

Diff: 2 Var: 1

Chapter/Section: Ch 07, Sec 02

Learning Objective: Use equality of matrices.

7) Calculate -4A - 5B if A = [table ( ( -6 -6 -9 )( -10 5 -10 ) )] and B = [table ( ( 10 6 8 )( -1 1 -4 ) )] .

A) [table ( ( 45 -25 60 )( -26 -6 -4 ) )]

B) [table ( ( -26 -6 -4 )( 45 -25 60 ) )]

C) [table ( ( -4 -6 -26 )( 60 -25 45 ) )]

D) [table ( ( 45 -6 -4 )( -26 -25 60 ) )]

Diff: 2 Var: 1

Chapter/Section: Ch 07, Sec 02

Learning Objective: Add and subtract matrices.; Perform scalar multiplication.

8) A company has two rubrics for scoring job applicants based on weighing education, experience, and the interview differently.

Matrix A

Rubric 1 Rubric 2

Education

Experience

Interview

[table ( ( _0.6 __ 0.3 )(_ 0.3__ 0.4 )(_ 0.1 __ 0.3 ) )__]

Applications receive a score from 1 to 10 in each category (education, experience, and interview). Two applicants are shown in matrix B:

Matrix B

Education Experience Interview

Applicant1

Applicant2

[table ( ( __8 __ 10 __ _ 1 __)(__ 10 __ 3 __ _ 2 __) )]

What is the order of BA? What does each entry in BA tell us?

BA = [table ( ( 7.9 6.7 )( 7.1 4.8 ) )]

Each entry tells the rubric scoring of each applicant.

Diff: 2 Var: 1

Chapter/Section: Ch 07, Sec 02

Learning Objective: Multiply two matrices.

9) Perform the indicated operations for the expression, if possible.

A = [table ( ( -10 )( 14 ) )] B = [table ( ( 11 -12 -15 ) )] C = [table ( ( -7 4 -4 )( 9 2 -1 ) )]

AB - 9C

A) [table ( ( 73 -186 -201 )( -47 84 186 ) )]

B) [table ( ( -47 73 )( 84 -186 )( 186 -201 ) )]

C) [table ( ( -47 84 186 )( 73 -186 -201 ) )]

D) not possible

Diff: 3 Var: 1

Chapter/Section: Ch 07, Sec 02

Learning Objective: Add and subtract matrices.; Multiply two matrices.; Perform scalar multiplication.

10) Perform the indicated operations for the expression, if possible.

A = [table ( ( -5 5 10 )( -4 -9 10 )( -8 8 -10 ) )] B = [table ( ( 10 2 -16 )( 2 3 -18 )( 1 -8 8 ) )]

(A) with superscript (2) - 3B

A) [table ( ( -105 -30 85 )( 4 132 -168 )( -52 -176 76 ) )]

B) [table ( ( -105 4 -52 )( -30 132 -176 )( 85 -168 76 ) )]

C) [table ( ( -5 19 148 )( 10 72 154 )( 61 88 76 ) )]

D) not possible

Diff: 3 Var: 1

Chapter/Section: Ch 07, Sec 02

Learning Objective: Add and subtract matrices.; Multiply two matrices.; Perform scalar multiplication.

11) Write the order of the matrix.

[table ( ( 4 2 1 )( -3 10 3 ) )]

A) 3 × 2

B) 2 × 2

C) 2 × 3

D) 3 × 3

Diff: 1 Var: 1

Chapter/Section: Ch 07, Sec 02

Learning Objective: Determine the order of a matrix.

12) Write the order of the matrix.

[table ( ( -9 5 )( -5 -8 )( 8 -6 ) )]

A) 3 × 3

B) 2 × 2

C) 2 × 3

D) 3 × 2

Diff: 1 Var: 1

Chapter/Section: Ch 07, Sec 02

Learning Objective: Determine the order of a matrix.

13) Write the order of the matrix.

[table ( ( 9 2 -10 -4 ) )]

A) 4 × 1

B) 4 × 4

C) 1 × 4

D) 1 × 1

Diff: 1 Var: 1

Chapter/Section: Ch 07, Sec 02

Learning Objective: Determine the order of a matrix.

14) Solve for the indicated variables.

[table ( (8x - 4y 1 )( 11 21 ) )] = [table ( ( 36 1 )( 11 5x - 3y) )]

A) (-6, 3)

B) (3, 6)

C) (6, 3)

D) (-6, -3)

Diff: 2 Var: 1

Chapter/Section: Ch 07, Sec 02

Learning Objective: Use equality of matrices.

15) Solve for the indicated variables.

[table ( ( x -1 )( 6 8 ) )] = [table ( ( 2 -1 )( 6 y ) )]

A) (-4, 5)

B) (-1, 6)

C) (2, 8)

D) (4, 5)

Diff: 2 Var: 1

Chapter/Section: Ch 07, Sec 02

Learning Objective: Use equality of matrices.

16) Solve for the indicated variables.

[table ( (4x - 7 (x) with superscript (2) )( (y) with superscript (2) 11 ) )] = [table ( ( 13 25 )( 16 3x - 2y) )]

A) (-5, -4)

B) (-4, 5)

C) (5, -4)

D) (-5, 4)

Diff: 2 Var: 1

Chapter/Section: Ch 07, Sec 02

Learning Objective: Use equality of matrices.

17) Calculate AB if A = [table ( ( -9 -3 7 )( 2 -4 1 ) )] and B = [table ( ( 1 )( 8 )( 4 ) )] .

Diff: 3 Var: 1

Chapter/Section: Ch 07, Sec 02

Learning Objective: Multiply two matrices.

18) Calculate (A) with superscript (2) if A = [table ( ( 8 9 )( 3 -3 ) )] .

A) [table ( ( 15 36 )( 91 45 ) )]

B) [table ( ( 36 15 )( 45 91 ) )]

C) [table ( ( 45 91 )( 36 15 ) )]

D) [table ( ( 91 45 )( 15 36 ) )]

Diff: 3 Var: 1

Chapter/Section: Ch 07, Sec 02

Learning Objective: Multiply two matrices.

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Chapter 7 Matrices

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Cynthia Y. Young

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