Matrices Young Chapter 7 Test Questions & Answers - Test Bank | College Algebra 5e by Young by Cynthia Y. Young. DOCX document preview.

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Matrices Young Chapter 7 Test Questions & Answers

College Algebra, 5e (Young)

Chapter 7 Matrices

7.1 Matrices and Systems of Linear Equations

1) Write the system of linear equations as an augmented matrix.

6x + 4y = -9

8x + 3y = 10

A) matrix ((6 8 4 3 -9 10))

B) augmented matrix ((6 4 -9)(8 3 10))

C) augmented matrix ((4 -9 6)(3 10 8))

D) augmented matrix ((6 -9 4)(8 10 3))

Diff: 1 Var: 1

Chapter/Section: Ch 07, Sec 01

Learning Objective: Write a system of linear equations as an augmented matrix.

2) Write the system of linear equations as an augmented matrix.

10x - 12y = 26

29x + 22y = -7

A) augmented matrix ((10 -12 29)(29 22 -7))

B) augmented matrix ((-12 10 26)(22 29 -7))

C) augmented matrix ((10 29 26)(-12 22 -7))

D) matrix ((26 -7 10 29 -12 22))

Diff: 1 Var: 1

Chapter/Section: Ch 07, Sec 01

Learning Objective: Write a system of linear equations as an augmented matrix.

3) Write the system of linear equations as an augmented matrix.

7x - 14y + 28z = -18

-28x + 26y - 23z = 13

-15x - 12y - 17z = -1

A) augmented matrix ((7 -28 -15 -18)(-14 26 -12 13)(28 -23 -17 -1))

B) augmented matrix ((7 -14 -18 28)(-28 26 13 -23)(-15 -12 -1 -17))

C) augmented matrix ((7 -14 28 -18)(-28 26 -23 13)(-15 -12 -17 -1))

D) augmented matrix ((-18 -14 28 7)(13 26 -23 -28)(-1 -12 -17 -15))

Diff: 1 Var: 1

Chapter/Section: Ch 07, Sec 01

Learning Objective: Write a system of linear equations as an augmented matrix.

4) Write the system of linear equations as an augmented matrix.

18x - 28y + 12z = -25

-17x + 29y + 16z = 11

27x - 25y - 23z = 14

A) augmented matrix ((18 -28 -25 12)(-17 29 11 16)(27 -25 14 -23))

B) augmented matrix ((18 -17 27 -25)(-28 29 -25 11)(12 16 -23 14))

C) augmented matrix ((18 28 12 -25)(-17 29 16 11)(27 25 23 14))

D) augmented matrix ((18 -28 12 -25)(-17 29 16 11)(27 -25 -23 14))

Diff: 1 Var: 1

Chapter/Section: Ch 07, Sec 01

Learning Objective: Write a system of linear equations as an augmented matrix.

5) Write the system of linear equations represented by the augmented matrix. Utilize the variables x and y.

augmented matrix ((14 7 30)(28 -2 16))

A) 14x - 7y = 30

28x + 2y = 16

B) 14x + 7y = 30

28x - 2y = 16

C) 28x + 7y = 30

14x - 2y = 16

D) 14x + 2y = 16

28x - 16y = 30

Diff: 1 Var: 1

Chapter/Section: Ch 07, Sec 01

Learning Objective: Write a system of linear equations as an augmented matrix.

6) Write the system of linear equations as represented by the augmented matrix. Utilize the variables x and y.

augmented matrix ((5 2 -12)(-6 7 -20))

A) -6x - 2y = -12

5x + 7y = -20

B) 5x - 2y = -20

-6x + 7y = -12

C) 5x + 7y = -12

-6x + 2y = -20

D) 5x - 2y = -12

-6x + 7y = -20

Diff: 1 Var: 1

Chapter/Section: Ch 07, Sec 01

Learning Objective: Write a system of linear equations as an augmented matrix.

7) Write the system of linear equations as represented by the augmented matrix. Utilize the variables x, y, and z.

augmented matrix ((-4 7 -2 15)(10 -18 19 -30)(20 12 17 9))

A) -4x + 7y - 2z = 15

10x - 18y + 19z = -30

20x + 12y + 17z = 9

B) -4x - 7y + 2z = 15

10x + 18y + 19z = -30

20x + 12y + 17z = 9

C) -4x + 7y - 2z = -15

10x - 18y + 19z = -30

20x - 12y - 17z = 9

D) -4x + 7y - 2z = -30

10x - 18y + 19z = 15

20x - 12y + 17z = 9

Diff: 1 Var: 1

Chapter/Section: Ch 07, Sec 01

Learning Objective: Write a system of linear equations as an augmented matrix.

8) Use row operations to transform the matrix to reduced row-echelon form.

augmented matrix ((7 -6 5)(4 5 45))

A) augmented matrix ((0 0 5)(1 1 5))

B) augmented matrix ((0 1 5)(0 1 5))

C) augmented matrix ((1 1 5)(0 0 5))

D) augmented matrix ((1 0 5)(0 1 5))

Diff: 2 Var: 1

Chapter/Section: Ch 07, Sec 01

Learning Objective: Perform row operations on an augmented matrix.; Write a matrix in reduced row-echelon form.; Write a matrix in row-echelon form.

9) Use row operations to transform the matrix to reduced row-echelon form.

augmented matrix ((1 7 -8 5)(-2 -8 1 -13)(7 1 7 2))

A) augmented matrix ((1 0 0 -1)(1 0 0 2)(1 0 0 1))

B) augmented matrix ((1 0 0 -1)(0 1 0 2)(0 0 1 1))

C) augmented matrix ((1 0 0 1)(0 1 0 2)(0 0 1 -1))

D) augmented matrix ((1 1 1 -1)(0 0 0 2)(0 0 0 1))

Diff: 3 Var: 1

Chapter/Section: Ch 07, Sec 01

Learning Objective: Perform row operations on an augmented matrix.; Write a matrix in reduced row-echelon form.; Write a matrix in row-echelon form.

10) Use row operations to transform the matrix to reduced row-echelon form.

augmented matrix ((2 6 6 -2)(7 3 -2 21)(9 7 6 13))

A) augmented matrix ((1 0 0 2)(1 0 0 1)(1 0 0 -2))

B) augmented matrix ((0 0 1 2)(0 1 0 1)(1 0 0 -2))

C) augmented matrix ((1 1 1 2)(0 0 0 1)(0 0 0 -2))

D) augmented matrix ((1 0 0 2)(0 1 0 1)(0 0 1 -2))

Diff: 3 Var: 1

Chapter/Section: Ch 07, Sec 01

Learning Objective: Perform row operations on an augmented matrix.; Write a matrix in reduced row-echelon form.; Write a matrix in row-echelon form.

11) Perform the row operation (R) with subscript (1) + (R) with subscript (2) → (R) with subscript (2) on the matrix and write the resulting matrix.

augmented matrix ((3 -10 9)(9 -11 -1))

A) augmented matrix ((3 -7 9)(9 -2 -1))

B) augmented matrix ((3 -10 9)(12 -21 8))

C) augmented matrix ((12 -21 8)(9 -11 -1))

D) augmented matrix ((-7 -10 9)(-2 -11 -1))

Diff: 3 Var: 1

Chapter/Section: Ch 07, Sec 01

Learning Objective: Perform row operations on an augmented matrix.

12) Perform the row operation -2(R) with subscript (1) + (R) with subscript (2) → (R) with subscript (2) on the matrix and write the resulting matrix.

augmented matrix ((7 -3 5)(8 -10 -3))

A) augmented matrix ((-14 6 -10)(-6 -4 -13))

B) augmented matrix ((7 -3 5)(-6 -4 -13))

C) augmented matrix ((-6 -4 -13)(8 -10 -3))

D) augmented matrix ((8 -10 -3)(-6 -4 -13))

Diff: 2 Var: 1

Chapter/Section: Ch 07, Sec 01

Learning Objective: Perform row operations on an augmented matrix.

13) Perform the row operation (R) with subscript (1) + (R) with subscript (2) → (R) with subscript (2) on the matrix and write the resulting matrix.

augmented matrix ((0 7 3 -14)(14 -15 -12 0)(10 7 -11 -5))

A) augmented matrix ((21 -15 -9 -14)(14 -15 -12 0)(10 7 -11 -5))

B) augmented matrix ((0 7 3 -14)(21 -15 -9 -14)(10 7 -11 -5))

C) augmented matrix ((14 -15 -12 0)(21 -15 -9 -14)(10 7 -11 -5))

D) augmented matrix ((21 -15 -9 -14)(0 7 3 -14)(10 7 -11 -5))

Diff: 2 Var: 1

Chapter/Section: Ch 07, Sec 01

Learning Objective: Perform row operations on an augmented matrix.

14) Perform the row operation -6(R) with subscript (1) + (R) with subscript (2) → (R) with subscript (2) on the matrix and write the resulting matrix.

augmented matrix ((10 -7 -5 -3)(-4 7 5 -10)(-5 -2 8 -10))

A) augmented matrix ((-64 49 35 8)(-4 7 5 -10)(-5 -2 8 -10))

B) augmented matrix ((-60 42 30 18)(-64 49 35 8)(-5 -2 8 -10))

C) augmented matrix ((10 -7 -5 -3)(-64 49 35 8)(-5 -2 8 -10))

D) augmented matrix ((10 -7 -5 -3)(-4 7 5 -10)(-5 -2 8 -10))

Diff: 2 Var: 1

Chapter/Section: Ch 07, Sec 01

Learning Objective: Perform row operations on an augmented matrix.

15) Perform the row operations -5(R) with subscript (1) + (R) with subscript (2) → (R) with subscript (2) and 4(R) with subscript (1) + (R) with subscript (3) → (R) with subscript (3) on the matrix and write the resulting matrix.

augmented matrix ((-7 2 0 1)(-5 8 10 3)(9 -3 -4 -3))

A) augmented matrix ((-7 2 0 1)(-5 8 10 3)(-19 5 -4 1))

B) augmented matrix ((-7 2 0 1)(30 -2 10 -2)(9 -3 -4 -3))

C) augmented matrix ((-7 2 0 1)(30 -2 10 -2)(-19 5 -4 1))

D) augmented matrix ((-7 2 0 1)(-19 5 -4 1)(30 -2 10 -2))

Diff: 2 Var: 1

Chapter/Section: Ch 07, Sec 01

Learning Objective: Perform row operations on an augmented matrix.

16) Use row operations to transform the matrix to reduced row-echelon form.

augmented matrix ((1 -8 -27)(10 -1 46))

A) augmented matrix ((1 0 5)(0 1 4))

B) augmented matrix ((0 0 5)(1 1 4))

C) augmented matrix ((1 1 5)(1 1 4))

D) augmented matrix ((0 1 5)(1 0 4))

Diff: 2 Var: 1

Chapter/Section: Ch 07, Sec 01

Learning Objective: Write a matrix in reduced row-echelon form.

17) Use row operations to transform the matrix to reduced row-echelon form.

augmented matrix ((8 -2 6 -52)(3 -6 6 -42)(9 8 -7 -21))

A) augmented matrix ((1 1 1 -6)(0 0 0 5)(0 0 0 1))

B) augmented matrix ((0 0 1 -6)(0 1 0 5)(1 0 0 1))

C) augmented matrix ((1 0 0 -6)(0 1 0 5)(0 0 1 1))

D) augmented matrix ((1 0 0 -6)(1 0 0 5)(1 0 0 1))

Diff: 3 Var: 1

Chapter/Section: Ch 07, Sec 01

Learning Objective: Write a matrix in reduced row-echelon form.

18) Solve the system of linear equations using Gaussian elimination with back-substitution.

-2x - 7y = -27

50x + 6y = 50

A) (5, -4)

B) (-4, 5)

C) (-2, -20)

D) (-20, -2)

Diff: 2 Var: 1

Chapter/Section: Ch 07, Sec 01

Learning Objective: Solve systems of linear equations using Gaussian elimination with back-substitution.

19) Solve the system of linear equations using Gaussian elimination with back-substitution.

5x + 8y + 8z = 29

2x + 8y + 3z = 31

2x + 4y + 6z = 12

A) (4, -1, 1)

B) (-1, 1, 4)

C) (1, -1, 4)

D) (1, 4, -1)

Diff: 3 Var: 1

Chapter/Section: Ch 07, Sec 01

Learning Objective: Solve systems of linear equations using Gaussian elimination with back-substitution.

20) Write the system of linear equations represented by the augmented matrix. Utilize the variables x, y, and z.

augmented matrix ((5 40 -29 -23)(28 33 -5 37)(42 13 42 12))

28x - 33y - 5z = 37

42x + 13y + 42z = 12

Diff: 1 Var: 1

Chapter/Section: Ch 07, Sec 01

Learning Objective: Write a system of linear equations as an augmented matrix.

21) Write the system of equations as represented by the augmented matrix. Utilize the variables x and y.

augmented matrix ((-8 22 -22)(15 -23 5))

15x - 23y = 5

Diff: 1 Var: 1

Chapter/Section: Ch 07, Sec 01

Learning Objective: Write a system of linear equations as an augmented matrix.

22) Perform the row operation 5(R) with subscript (1) + (R) with subscript (2) → (R) with subscript (2) on the matrix and write the resulting matrix.

augmented matrix ((10 -7 -2 10)(-22 23 22 6)(-19 -10 -1 12))

Diff: 2 Var: 1

Chapter/Section: Ch 07, Sec 01

Learning Objective: Perform row operations on an augmented matrix.

23) Use row operations to transform the matrix to reduced form.

augmented matrix ((-15 -17 15 -188)(20 -12 1 -56)(16 4 -7 72))

Diff: 3 Var: 1

Chapter/Section: Ch 07, Sec 01

Learning Objective: Perform row operations on an augmented matrix.; Write a matrix in reduced row-echelon form.

24) Brian and Beatrice decide to place $18,200 of their savings into investments. They put some in a money market account earning 4.5% interest, some in a mutual fund that has been averaging 5.7% a year, and some in a stock that rose 8.1% last year. If they put $4000 more in the money market than in the mutual fund and the mutual fund and stocks have the same growth in the next year as they did in the previous year, they will earn $1036.20 in a year. How much money did they put in each of the three investments?

A) $3100 at 4.5%, $7100 at 5.7%, $8000 at 8.1%

B) $8900 at 4.5%, $4900 at 5.7%, $4400 at 8.1%

C) $4900 at 4.5%, $4400 at 5.7%, $8900 at 8.1%

D) $7100 at 4.5%, $8000 at 5.7%, $3100 at 8.1%

Diff: 3 Var: 1

Chapter/Section: Ch 07, Sec 01

Learning Objective: Write a system of linear equations as an augmented matrix.

25) Josh and Ann decide to place $12,200 of their savings into investments. They put some in a money market account earning 2.7% interest, some in a mutual fund that has been averaging 5.9% a year, and some in a stock that rose 9.7% last year. If they put $1,200 more in the money market than in the mutual fund and the mutual fund and stocks have the same growth in the next year as they did in the previous year, they will earn $915.80 in a year. How much money did they put in each of the three investments?

Diff: 3 Var: 1

Chapter/Section: Ch 07, Sec 01

Learning Objective: Write a system of linear equations as an augmented matrix.

26) Find the values of a, b, and c such that the graph of the quadratic function y = a(x) with superscript (2) + bx + c passes through the points (2, -1), (-4, 83), and (4, 35).

Diff: 3 Var: 1

Chapter/Section: Ch 07, Sec 01

Learning Objective: Write a system of linear equations as an augmented matrix.

27) Write the order of the matrix.

matrix ((-7 10 9 5 -9 7))

A) 3 × 2

B) 2 × 2

C) 2 × 3

D) 3 × 3

Diff: 1 Var: 1

Chapter/Section: Ch 07, Sec 01

Learning Objective: Determine the order of a matrix.

28) Write the order of the matrix.

[table ( ( -2 10 )( -9 5 )( 4 0 ) )]

A) 3 × 3

B) 2 × 2

C) 2 × 3

D) 3 × 2

Diff: 1 Var: 1

Chapter/Section: Ch 07, Sec 01

Learning Objective: Determine the order of a matrix.

29) Solve the system of linear equations for x, y, and z using Gauss-Jordan elimination.

table ( (3x + 7y = 2)(4x - 8y - 8z = 36)(8x - 3y - 4z = 35) )

A) (3, -1, -2)

B) (3, 1, -2)

C) (-2, -1, 3)

D) (-2, 1, 3)

Diff: 3 Var: 1

Chapter/Section: Ch 07, Sec 01

Learning Objective: Solve systems of linear equations using Gauss-Jordan elimination.

30) Solve the system of linear equations for x, y, and z using Gauss-Jordan elimination.

table ( (2x + 4z = -8)(7x + 2y - 2z = 28)( -2y + 6z = -26) )

A) (-2, 4, -3)

B) (-3, 4, 2)

C) (2, 4, -3)

D) (4, -3, 2)

Diff: 3 Var: 1

Chapter/Section: Ch 07, Sec 01

Learning Objective: Solve systems of linear equations using Gauss-Jordan elimination.

31) Solve the system of linear equations for x, y, and z using Gauss-Jordan elimination.

3x - 7y + 2z = -37

8x - 2y - 6z = 12

-5x + 7y + 2z = 35

Diff: 3 Var: 1

Chapter/Section: Ch 07, Sec 01

Learning Objective: Solve systems of linear equations using Gauss-Jordan elimination.

32) Solve the system of linear equations using Gaussian elimination with back-substitution.

table ( (6x + 8y = -14)(7x - 7y - 3z = 46)(7x - 2y - 7z = 22) )

A) (3, -4, 1)

B) (3, 4, 1)

C) (1, -4, 3)

D) (1, 4, 3)

Diff: 3 Var: 1

Chapter/Section: Ch 07, Sec 01

Learning Objective: Solve systems of linear equations using Gaussian elimination with back-substitution.

33) Write the order of the matrix.

[table ( ( -8 4 -5 )( 3 5 -2 ) )]

A) 3 × 2

B) 2 × 2

C) 2 × 3

D) 3 × 3

Diff: 1 Var: 1

Chapter/Section: Ch 07, Sec 01

Learning Objective: Determine the order of a matrix.

34) Write the order of the matrix.

[table ( ( -7 10 )( -1 -10 )( 2 -2 ) )]

A) 3 × 3

B) 2 × 2

C) 2 × 3

D) 3 × 2

Diff: 1 Var: 1

Chapter/Section: Ch 07, Sec 01

Learning Objective: Determine the order of a matrix.

35) Write the order of the matrix.

[table ( ( -5 3 4 -10 ) )]

A) 4 × 1

B) 4 × 4

C) 1 × 4

D) 1 × 1

Diff: 1 Var: 1

Chapter/Section: Ch 07, Sec 01

Learning Objective: Determine the order of a matrix.

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Document Type:
DOCX
Chapter Number:
7
Created Date:
Aug 21, 2025
Chapter Name:
Chapter 7 Matrices
Author:
Cynthia Y. Young

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