Edrftgyihu jiuh
Linear Algebra: A
Modern Introduction
ST
5th Edition
UV
TEST BANK
IA
_A
David Poole
PP
────────────────────────────────────────────────────
Comprehensive Test Bank for Instructors and
Students
RO
© David Poole. All rights reserved. Reproduction
or distribution without permission is prohibited.
VE
D?
||| ||| || ||| || | || ||| | || ||| |
9798214013053
© MEDCONNOISSEUR
, Edrftgyihu jiuh
Test Bank — Linear Algebra: A Modern Introduction, 5th
Edition
Author: David Poole
ISBN: 9798214013053
ST
Chapter 1: Vectors
Chapter 2: Systems of Linear Equations
UV
Chapter 3: Matrices
Chapter 4: Eigenvalues and Eigenvectors
Chapter 5: Orthogonality
Chapter 6: Vector Spaces
IA
Chapter 7: Distance and Approximation
Chapter 8: Codes
_A
PP
RO
VE
D?
© MEDCONNOISSEUR
, Test Bank For
Linear Algebra A Modern Introduction 5th Edition by David Poole Copyright 2026
Section 1.0 - 1.4
ST
1. If u • v = 0, then ||u + v|| = ||u – v||.
a. True
b. False
UV
2. If u • v = u • w, then either u = 0 or v = w.
a. True
b. False
3. a • b × c = 0 if and only if the vectors a, b, c are coplanar.
a. True
IA
b. False
n
4. The distance between two points in located by the vectors u and v is ||u – v||.
_A
a. True
b. False
5. If v is any nonzero vector, then 6v is a vector in the same direction as v with a length of 6 units.
a. True
PP
b. False
6. The only real number c for which [c, –2, 1] is orthogonal to [2c, c, –4] is c = 2.
a. True
b. False
RO
7. The projection of a vector v onto a vector u is undefined if v = 0.
a. True
b. False
VE
8. The area of the parallelogram with sides a, b, is || ||
a. True
b. False
D?
2 2 2 2
9. If a, b, c are mutually orthogonal vectors in , then (a × b • c) = ||a|| ||b|| ||c|| .
a. True
b. False
10. For all vectors v and scalars c, ||cv|| = c||v||.
a. True
b. False
Copyright Cengage Learning. Powered by Cognero. Page 1
, n
11. For all vectors u, v, w in , u – (v – w) = u + w – v.
a. True
b. False
12. The projection of a vector v onto a vector u is undefined if u = 0.
ST
a. True
b. False
13. The vectors [1, 2, 3] and [k, 2k, 3k] have the same direction for all nonzero real numbers k?
UV
a. True
b. False
14. If a parity check code is used in the transmission of a message consisting of a binary vector, then the total number of
1’s in the message will be even.
a. True
IA
b. False
15. The distance between the planes n • x = d1 and n • x = d2 is |d1 – d2|.
a. True
_A
b. False
16. The zero vector is orthogonal to every vector except itself.
a. True
b. False
PP
17. The products a × (b × c) and (a × b) × c are equal if and only if b = 0.
a. True
b. False
RO
18. Simplify the following vector expression: 4u – 2(v + 3w) + 6(w u).
VE
19. Find all solutions of 3x + 5 = 2 in , or show that there are no solutions.
a. 2
b. 4
c. 6
d. 8
D?
20. Find the distance between the parallel lines.
and
21. Find the acute angle between the planes 3 and .
Copyright Cengage Learning. Powered by Cognero. Page 2
Linear Algebra: A
Modern Introduction
ST
5th Edition
UV
TEST BANK
IA
_A
David Poole
PP
────────────────────────────────────────────────────
Comprehensive Test Bank for Instructors and
Students
RO
© David Poole. All rights reserved. Reproduction
or distribution without permission is prohibited.
VE
D?
||| ||| || ||| || | || ||| | || ||| |
9798214013053
© MEDCONNOISSEUR
, Edrftgyihu jiuh
Test Bank — Linear Algebra: A Modern Introduction, 5th
Edition
Author: David Poole
ISBN: 9798214013053
ST
Chapter 1: Vectors
Chapter 2: Systems of Linear Equations
UV
Chapter 3: Matrices
Chapter 4: Eigenvalues and Eigenvectors
Chapter 5: Orthogonality
Chapter 6: Vector Spaces
IA
Chapter 7: Distance and Approximation
Chapter 8: Codes
_A
PP
RO
VE
D?
© MEDCONNOISSEUR
, Test Bank For
Linear Algebra A Modern Introduction 5th Edition by David Poole Copyright 2026
Section 1.0 - 1.4
ST
1. If u • v = 0, then ||u + v|| = ||u – v||.
a. True
b. False
UV
2. If u • v = u • w, then either u = 0 or v = w.
a. True
b. False
3. a • b × c = 0 if and only if the vectors a, b, c are coplanar.
a. True
IA
b. False
n
4. The distance between two points in located by the vectors u and v is ||u – v||.
_A
a. True
b. False
5. If v is any nonzero vector, then 6v is a vector in the same direction as v with a length of 6 units.
a. True
PP
b. False
6. The only real number c for which [c, –2, 1] is orthogonal to [2c, c, –4] is c = 2.
a. True
b. False
RO
7. The projection of a vector v onto a vector u is undefined if v = 0.
a. True
b. False
VE
8. The area of the parallelogram with sides a, b, is || ||
a. True
b. False
D?
2 2 2 2
9. If a, b, c are mutually orthogonal vectors in , then (a × b • c) = ||a|| ||b|| ||c|| .
a. True
b. False
10. For all vectors v and scalars c, ||cv|| = c||v||.
a. True
b. False
Copyright Cengage Learning. Powered by Cognero. Page 1
, n
11. For all vectors u, v, w in , u – (v – w) = u + w – v.
a. True
b. False
12. The projection of a vector v onto a vector u is undefined if u = 0.
ST
a. True
b. False
13. The vectors [1, 2, 3] and [k, 2k, 3k] have the same direction for all nonzero real numbers k?
UV
a. True
b. False
14. If a parity check code is used in the transmission of a message consisting of a binary vector, then the total number of
1’s in the message will be even.
a. True
IA
b. False
15. The distance between the planes n • x = d1 and n • x = d2 is |d1 – d2|.
a. True
_A
b. False
16. The zero vector is orthogonal to every vector except itself.
a. True
b. False
PP
17. The products a × (b × c) and (a × b) × c are equal if and only if b = 0.
a. True
b. False
RO
18. Simplify the following vector expression: 4u – 2(v + 3w) + 6(w u).
VE
19. Find all solutions of 3x + 5 = 2 in , or show that there are no solutions.
a. 2
b. 4
c. 6
d. 8
D?
20. Find the distance between the parallel lines.
and
21. Find the acute angle between the planes 3 and .
Copyright Cengage Learning. Powered by Cognero. Page 2
