Test Bank – Linear Algebra: A Modern Introduction, 5th Edition – David Poole – ISBN 9798214013053 (All Chapters Covered 1–8)

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Linear Algebra: A
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Modern Introduction
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5th Edition
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TEST BANK
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David Poole
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Comprehensive Test Bank for Instructors
and Students
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9798214013053


© David Poole. All rights reserved. Reproduction
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or distribution without permission is prohibited.
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Linear Algebra: A Modern Introduction — Test Bank
David Poole
ISBN: 9798214013053
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Chapter 1: Vectors (geometry and dot products)
Chapter 2: Systems of Linear Equations (Gaussian elimination and spanning sets)
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Chapter 3: Matrices (inverses, LU factorization, and Markov chains)
Chapter 4: Eigenvalues and Eigenvectors (determinants and diagonalization)
Chapter 5: Orthogonality (Gram-Schmidt process and QR factorization)
Chapter 6: Vector Spaces (basis, dimension, and linear transformations)
Chapter 7: Distance and Approximation (least squares and SVD)
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Chapter 8: Codes (error-detecting and error-correcting codes)
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, Test Bank For
Linear Algebra A Modern Introduction 5th Edition by David Poole Copyright 2026
Section 1.0 - 1.4
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1. If u • v = 0, then ||u + v|| = ||u – v||.
a. True
b. False
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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.
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a. True
b. False

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4. The distance between two points in located by the vectors u and v is ||u – v||.
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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.
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a. True
b. False

6. The only real number c for which [c, –2, 1] is orthogonal to [2c, c, –4] is c = 2.
a. True
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b. False

7. The projection of a vector v onto a vector u is undefined if v = 0.
a. True
b. False
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8. The area of the parallelogram with sides a, b, is || ||

a. True
b. False
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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
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10. For all vectors v and scalars c, ||cv|| = c||v||.
a. True
b. False
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11. For all vectors u, v, w in , u – (v – w) = u + w – v.
a. True
b. False
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12. The projection of a vector v onto a vector u is undefined if u = 0.
a. True
b. False
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13. The vectors [1, 2, 3] and [k, 2k, 3k] have the same direction for all nonzero real numbers k?
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.
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a. True
b. False

15. The distance between the planes n • x = d1 and n • x = d2 is |d1 – d2|.
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a. True
b. False

16. The zero vector is orthogonal to every vector except itself.
a. True
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b. False

17. The products a × (b × c) and (a × b) × c are equal if and only if b = 0.
a. True
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b. False




18. Simplify the following vector expression: 4u – 2(v + 3w) + 6(w u).
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19. Find all solutions of 3x + 5 = 2 in , or show that there are no solutions.
a. 2
b. 4
c. 6
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d. 8

20. Find the distance between the parallel lines.
and
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21. Find the acute angle between the planes 3 and .


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