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,Copyright Cengage Learning. Powered by Cognero.
zl zl zl zl zl Page 2
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, Test Bank For zl zl
Linear Algebra A Modern Introduction 5th Edition by David Poole Copyright 2026
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Section 1.0 - 1.4 zl zl zl
1. If u • v = 0, then ||u + v|| = ||u – v||.
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a. True
b. False
2. If u • v = u • w, then either u = 0 or v = w.
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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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located by the vectors u and v is ||u – v||.
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4. The distance between two points in
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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.
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a. True
b. False
7. The projection of a vector v onto a vector u is undefined if v = 0.
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a. True
b. False
8. The area of the parallelogram with sides a, b, is
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a. True
b. False
2 2 2 2
, then (a × b • c) = ||a|| ||b|| ||c|| .
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9. If a, b, c are mutually orthogonal vectors in
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a. True
b. False
10. For all vectors v and scalars c, ||cv|| = c||v||.
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a. True
b. False
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11. For all vectors u, v, w in
zl zl zl zl zl zl zl , u – (v – w) = u + w – v.
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a. True
b. False
12. The projection of a vector v onto a vector u is undefined if u = 0.
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a. True
b. False
13. The vectors [1, 2, 3] and [k, 2k, 3k] have the same direction for all nonzero real numbers k?
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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
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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.
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a. True
b. False
17. The products a × (b × c) and (a × b) × c are equal if and only if b = 0.
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a. True
b. False
18. Simplify the following vector expression: 4u – 2(v + 3w) + 6(w
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19. Find all solutions of 3x + 5 = 2 in
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a. 2z l
b. 4z l
c. 6z l
d. 8z l
Find the distance between the parallel lines.
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20.
and
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21. Find the acute angle between the planes
zl zl zl zl zl zl zl zl 3 andzl zl .
Copyright Cengage Learning. Powered by Cognero.
zl zl zl zl zl Page 4zl
zl zl zl zl zl Page 1
zl
,Copyright Cengage Learning. Powered by Cognero.
zl zl zl zl zl Page 2
zl
, Test Bank For zl zl
Linear Algebra A Modern Introduction 5th Edition by David Poole Copyright 2026
zl zl zl zl zl zl zl zl zl zl zl
Section 1.0 - 1.4 zl zl zl
1. If u • v = 0, then ||u + v|| = ||u – v||.
zl zl zl zl zl zl zl zl zl zl zl zl zl
a. True
b. False
2. If u • v = u • w, then either u = 0 or v = w.
zl zl zl zl zl zl zl zl zl zl zl zl zl zl zl zl
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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located by the vectors u and v is ||u – v||.
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4. The distance between two points in
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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.
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a. True
b. False
7. The projection of a vector v onto a vector u is undefined if v = 0.
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a. True
b. False
8. The area of the parallelogram with sides a, b, is
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a. True
b. False
2 2 2 2
, then (a × b • c) = ||a|| ||b|| ||c|| .
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9. If a, b, c are mutually orthogonal vectors in
zl zl zl zl zl zl zl zl zl zl zl zl zl zl zl zl
a. True
b. False
10. For all vectors v and scalars c, ||cv|| = c||v||.
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a. True
b. False
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, n
11. For all vectors u, v, w in
zl zl zl zl zl zl zl , u – (v – w) = u + w – v.
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a. True
b. False
12. The projection of a vector v onto a vector u is undefined if u = 0.
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a. True
b. False
13. The vectors [1, 2, 3] and [k, 2k, 3k] have the same direction for all nonzero real numbers k?
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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
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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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zl
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a. True
b. False
16. The zero vector is orthogonal to every vector except itself.
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a. True
b. False
17. The products a × (b × c) and (a × b) × c are equal if and only if b = 0.
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a. True
b. False
18. Simplify the following vector expression: 4u – 2(v + 3w) + 6(w
zl zl zl zl zl zl zl zl zl zl zl zl zl u).
19. Find all solutions of 3x + 5 = 2 in
zl zl zl zl zl zl zl zl zl zl , or show that there are no solutions.
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a. 2z l
b. 4z l
c. 6z l
d. 8z l
Find the distance between the parallel lines.
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20.
and
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21. Find the acute angle between the planes
zl zl zl zl zl zl zl zl 3 andzl zl .
Copyright Cengage Learning. Powered by Cognero.
zl zl zl zl zl Page 4zl
