Complete Test Bank Matrices Chapter.7 5th Edition

College Algebra, 5e (Young)

Chapter 7 Matrices

7.4 The Determinant of a Square Matrix and Cramer's Rule

1) Evaluate the 2 × 2 determinant.

A) 23

B) -23

C) -26

D) 26

Diff: 1 Var: 1

Chapter/Section: Ch 07, Sec 04

Learning Objective: Find the determinant of a 2 x 2 matrix.

2) Evaluate the 2 × 2 determinant.

A) 27

B) -27

C) -37

D) 37

Diff: 1 Var: 1

Chapter/Section: Ch 07, Sec 04

Learning Objective: Find the determinant of a 2 x 2 matrix.

3) Evaluate the 2 × 2 determinant.

A) 6

B) -2

C) -6

D) 2

Diff: 1 Var: 1

Chapter/Section: Ch 07, Sec 04

Learning Objective: Find the determinant of a 2 x 2 matrix.

4) Evaluate the 2 × 2 determinant.

A) -15.88

B) 11.32

C) 15.88

D) -1.3

Diff: 1 Var: 1

Chapter/Section: Ch 07, Sec 04

Learning Objective: Find the determinant of a 2 x 2 matrix.

5) Evaluate the 2 × 2 determinant.

A) -13.92

B) -9.6

C) 14.4

D) 13.92

Diff: 1 Var: 1

Chapter/Section: Ch 07, Sec 04

Learning Objective: Find the determinant of a 2 x 2 matrix.

6) Evaluate the 2 × 2 determinant.

A) -51.16

B) 51.16

C) 4.9

D) -5.24

Diff: 1 Var: 1

Chapter/Section: Ch 07, Sec 04

Learning Objective: Find the determinant of a 2 x 2 matrix.

7) Evaluate the 2 × 2 determinant.

A) -

B)

C) -

D)

Diff: 2 Var: 1

Chapter/Section: Ch 07, Sec 04

Learning Objective: Find the determinant of a 2 x 2 matrix.

8) Evaluate the 2 × 2 determinant.

A)

B)

C) -

D) -

Diff: 2 Var: 1

Chapter/Section: Ch 07, Sec 04

Learning Objective: Find the determinant of a 2 x 2 matrix.

9) Evaluate the 2 × 2 determinant.

A) 36

B) 0

C) -36

D) 10

Diff: 1 Var: 1

Chapter/Section: Ch 07, Sec 04

Learning Objective: Find the determinant of a 2 x 2 matrix.

10) Use Cramer's Rule to either solve the system of equations, determine if the system is inconsistent (no solutions), or dependent (infinitely many solutions).

-5x - 4y = -13

-2x - 2y = -4

A) (-3, 5)

B) (5, -3)

C) inconsistent

D) dependent

Diff: 2 Var: 1

Chapter/Section: Ch 07, Sec 04

Learning Objective: Use Cramer's rule to solve a square system of linear equations.

11) Use Cramer's Rule to either solve the system of equations, determine if the system is inconsistent (no solutions), or dependent (infinitely many solutions).

-4x - 8y = -32

4x + 8y = 32

A) (2, 4)

B) (4, 2)

C) inconsistent

D) dependent

Diff: 2 Var: 1

Chapter/Section: Ch 07, Sec 04

Learning Objective: Use Cramer's rule to solve a square system of linear equations.

12) Use Cramer's Rule to either solve the system of equations, determine if the system is inconsistent (no solutions), or dependent (infinitely many solutions).

5x + 10y = 80

20x + 40y = -320

A) (8, 6)

B) (6, 8)

C) inconsistent

D) dependent

Diff: 2 Var: 1

Chapter/Section: Ch 07, Sec 04

Learning Objective: Use Cramer's rule to solve a square system of linear equations.

13) Evaluate the 3 × 3 determinant.

A) 164

B) 248

C) -268

D) -296

Diff: 3 Var: 1

Chapter/Section: Ch 07, Sec 04

Learning Objective: Find the determinant of a n x n matrix.

14) Evaluate the 3 × 3 determinant.

A) -492

B) 768

C) 408

D) 492

Diff: 3 Var: 1

Chapter/Section: Ch 07, Sec 04

Learning Objective: Find the determinant of a n x n matrix.

15) Evaluate the 3 × 3 determinant.

A) -334

B) 170

C) 158

D) 14

Diff: 3 Var: 1

Chapter/Section: Ch 07, Sec 04

Learning Objective: Find the determinant of a n x n matrix.

16) Use Cramer's Rule to either solve the system of equations, determine if the system is inconsistent (no solution), or dependent (infinitely many solutions).

-4x - 2y + 7z = -9

-5x - 3y + 6z = -5

5x + 8y - 7z = 28

A) (-3, 4, -5)

B) (-5, 4, -3)

C) inconsistent

D) dependent

Diff: 3 Var: 1

Chapter/Section: Ch 07, Sec 04

Learning Objective: Use Cramer's rule to solve a square system of linear equations.

17) Use Cramer's Rule to either solve the system of equations, determine if the system is inconsistent (no solution), or dependent (infinitely many solutions).

5x + 8y - 9z = 95

-5x - 8y + 9z = -95

9x + 10y + 8z = -45

A) (2, 5, 5)

B) (3, -4, -4)

C) inconsistent

D) dependent

Diff: 3 Var: 1

Chapter/Section: Ch 07, Sec 04

Learning Objective: Use Cramer's rule to solve a square system of linear equations.

18) Use Cramer's Rule to either solve the system of equations, determine if the system is inconsistent (no solution), or dependent (infinitely many solutions).

3x - 10y + 9z = -36

-3x + 10y - 9z = 10

4x + 6y - 4z = 26

A) (1, 3, -1)

B) (-1, 3, 1)

C) inconsistent

D) dependent

Diff: 3 Var: 1

Chapter/Section: Ch 07, Sec 04

Learning Objective: Use Cramer's rule to solve a square system of linear equations.

19) Evaluate the 2 × 2 determinant.

Diff: 1 Var: 1

Chapter/Section: Ch 07, Sec 04

Learning Objective: Find the determinant of a 2 x 2 matrix.

20) Use Cramer's Rule to solve the system of equations or determine if the system is inconsistent (no solution) or dependent (infinitely many solutions).

10x + 7y = -8

-10x - 7y = 8

Diff: 1 Var: 1

Chapter/Section: Ch 07, Sec 04

Learning Objective: Use Cramer's rule to solve a square system of linear equations.

21) Evaluate the 3 × 3 determinant.

Diff: 3 Var: 1

Chapter/Section: Ch 07, Sec 04

Learning Objective: Find the determinant of a n x n matrix.

22) Apply determinants to find the area of a triangle with vertices (10, 5), (-1, 12), and

A) 28 square units

B) 56 square units

C) 193 square units

D) 68 square units

Diff: 2 Var: 1

Chapter/Section: Ch 07, Sec 04

Learning Objective: Find the determinant of a n x n matrix.

23) Use Cramer's Rule to solve the system of equations or determine if the system is inconsistent (no solution) or dependent (infinitely many solutions).

x - y = -11

x + y = 11

Diff: 2 Var: 1

Chapter/Section: Ch 07, Sec 04

Learning Objective: Use Cramer's rule to solve a square system of linear equations.

24) Use Cramer's Rule to solve the system of equations or determine if the system is inconsistent (no solution) or dependent (infinitely many solutions).

x - y = 0

x + y = -48

Diff: 2 Var: 1

Chapter/Section: Ch 07, Sec 04

Learning Objective: Use Cramer's rule to solve a square system of linear equations.

25) Use Cramer's Rule to solve the system of equations or determine if the system is inconsistent (no solution) or dependent (infinitely many solutions).

2z - 8w = -34

2z - 8w = 6

A) (2, 8)

B) (-34, 6)

C) inconsistent

D) dependent

Diff: 2 Var: 1

Chapter/Section: Ch 07, Sec 04

Learning Objective: Use Cramer's rule to solve a square system of linear equations.

26) Use Cramer's Rule to solve the system of equations or determine if the system is inconsistent (no solution) or dependent (infinitely many solutions).

-9p - 8q = -22

-18p - 16q = -44

A) (6, -4)

B) (1, 8)

C) dependent

D) inconsistent

Diff: 2 Var: 1

Chapter/Section: Ch 07, Sec 04

Learning Objective: Use Cramer's rule to solve a square system of linear equations.

27) Use Cramer's Rule to solve the system of equations or determine if the system is inconsistent (no solution) or dependent (infinitely many solutions).

9.1t - 3.3u = -106.1

2t + 4.9u = 0.87

Diff: 2 Var: 1

Chapter/Section: Ch 07, Sec 04

Learning Objective: Use Cramer's rule to solve a square system of linear equations.

28) Use Cramer's Rule to solve the system of equations or determine if the system is inconsistent (no solution) or dependent (infinitely many solutions).

Diff: 3 Var: 1

Chapter/Section: Ch 07, Sec 04

Learning Objective: Use Cramer's rule to solve a square system of linear equations.

29) Use Cramer's Rule to solve the system of equations or determine if the system is inconsistent (no solution) or dependent (infinitely many solutions).

A) (-3, 3, -1)

B) (-3, -3, -1)

C) (-1, 3, -3)

D) (-1, -3, -3)

Diff: 3 Var: 1

Chapter/Section: Ch 07, Sec 04

Learning Objective: Use Cramer's rule to solve a square system of linear equations.

30) Solve the system of linear equations for x, y, and z.

Diff: 1 Var: 1

Chapter/Section: Ch 07, Sec 04

Learning Objective: Use Cramer's rule to solve a square system of linear equations.

31) Three points are collinear if the area of the triangle with vertices at those three points is zero. Are the points (10, -2), (5, -7), and (2, -13) colinear?

Diff: 2 Var: 1

Chapter/Section: Ch 07, Sec 04

Learning Objective: Find the determinant of a n x n matrix.

32) Three points are collinear if the area of the triangle with vertices at those three points is zero. Are the points (-18, 17), (-9, 9), and (27, -23) colinear?

Diff: 2 Var: 1

Chapter/Section: Ch 07, Sec 04

Learning Objective: Find the determinant of a n x n matrix.

33) Use Cramer's Rule to either solve the system of equations, determine if the system is inconsistent (no solutions), or dependent (infinitely many solutions).

-12x - 2y = -26

60x + 10y = 130

A) (7, 1)

B) (1, 7)

C) inconsistent

D) dependent

Diff: 2 Var: 1

Chapter/Section: Ch 07, Sec 04

Learning Objective: Use Cramer's rule to solve a square system of linear equations.

34) Use Cramer's Rule to either solve the system of equations, determine if the system is inconsistent (no solution), or dependent (infinitely many solutions).

A) (5, -1, -2)

B) (5, 2, 5)

C) inconsistent

D) dependent

Diff: 3 Var: 1

Chapter/Section: Ch 07, Sec 04

Learning Objective: Use Cramer's rule to solve a square system of linear equations.

© (2022) John Wiley & Sons, Inc. All rights reserved. Instructors who are authorized users of this course are permitted to download these materials and use them in connection with the course. Except as permitted herein or by law, no part of these materials should be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise.