TEST BANK FOR Linear Algebra: A Modern Introduction 5th Edition by David Poole ISBN:978-8214013054 COMPLETE GUIDE ALL CHAPTERS COVERED 100% VERIFIED A+ GRADE ASSURED!!!!!NEW LATEST UPDATE!!!!!

Test Bank For br br




Linear Algebra A Modern Introduction 5th Edition by David Poole Copyright 2026
br br br br br br br br br br br




Section 1.0 - 1.4 br br br




1. If u • v = 0, then ||u + v|| = ||u – v||.
br br br br br br br br br br br br br



a. True
b. False

2. If u • v = u • w, then either u = 0 or v = w.
br br br br br br br br br br br br br br br br



a. True
b. False

3. a • b × c = 0 if and only if the vectors a, b, c are coplanar.
br br br br br br br br br br br br br br br br br



a. True
b. False

n
located by the vectors u and v is ||u – v||.
br

4. The distance between two points in
br br br br br br br br br br br br br br br br




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.
br br br br br br br br br br br br br br br br br br br br br br



a. True
b. False

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



a. True
b. False

7. The projection of a vector v onto a vector u is undefined if v = 0.
br br br br br br br br br br br br br br br



a. True
b. False


8. The area of the parallelogram with sides a, b, is
br br br br br br br br br b r br || br ||

a. True
b. False

2 2 2 2
, then (a × b • c) = ||a|| ||b|| ||c|| .
br

9. If a, b, c are mutually orthogonal vectors in
br br br br br br br br br br br br br br br br




a. True
b. False

10. For all vectors v and scalars c, ||cv|| = c||v||.
br br br br br br br br br



a. True
b. False
Copyright Cengage Learning. Powered by Cognero.
br br br br br Page 1
br

, n
11. For all vectors u, v, w in
br br br br br br br , u – (v – w) = u + w – v.
br br br br br br br br br br br




a. True
b. False

12. The projection of a vector v onto a vector u is undefined if u = 0.
br br br br br br br br br br br br br br br



a. True
b. False

13. The vectors [1, 2, 3] and [k, 2k, 3k] have the same direction for all nonzero real numbers k?
br br br br br br br br br br br br br br br br br br



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
br br br br br br br br br br br br br br br br br br br br br br br



’s in the message will be even.
br br br br br br



a. True
b. False

15. The distance between the planes n • x = d1 and n • x = d2 is |d1 – d2|.
br br br br br br br br br
br
br br br br br
br
br
br
br



a. True
b. False

16. The zero vector is orthogonal to every vector except itself.
br br br br br br br br br



a. True
b. False

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



a. True
b. False




18. Simplify the following vector expression: 4u – 2(v + 3w) + 6(w
br br br br br br br br br br br br br u).


19. Find all solutions of 3x + 5 = 2 in
br br br br br br br br br br , or show that there are no solutions.
br br br br br br br




a. 2
b r



b. 4
b r



c. 6
b r



d. 8
b r




Find the distance between the parallel lines.
br br br br br br br


20.
and
br br




21. Find the acute angle between the planes
br br br br br br br br 3 and br br .


Copyright Cengage Learning. Powered by Cognero.
br br br br br Page 2 br

,22. Find the distance between the planes br br br br br br b r and br .

23. Find values of the scalar k for which the following vectors are orthogonal.
br br br br br br br br br br br br



u = [k, k, –2], v = [–2, k – 1, 5]
br br br br br br br br br br br




24. Simplify the following expressions: br br br



(a) (a + b + c) × c + (a + b + c) × b + (b – c) × a
br br br br br br br br br br br br br br br br br br br br



(b) (v + 2w) ∙ (w + z) × (3z + v)
br br br br br br br br br br




25. Find the check digit that should be appended to the vector u = [2, 5, 6, 4, 5] in
br br br br br br br br br br br br br br br br br br br br if the check vector is c = [1, 1, 1, 1,
br br br br br br br br br br




1, 1]. br




26. If u is orthogonal to v, then which of the following is also orthogonal to v?
br br br br br br br br br br br br br br br




27. What is the distance of the point P = (2, 3, –1) to the line of intersection of the planes 2x – 2y + z = –3 and 3x –
br br br br br br br br br br br br br br br br br br br br br br br br br br br br br



2y + 2z = –17?
br br br br br




28. In a parallelogram ABCD let
br br br br br br = a, br br br b. Let M be the point of intersection of the diagonals. Express
br br br br br br br br br br br br , br




br and b r b r as linear combinations of a and b.
br br br br br br




29. Suppose that the dot product of u = [u1, u2] and v = [v1, v2] in br br br br br br br br br br br br br br br br



2 br

were defined as u · v = 5u1 v1 + 2u2 v2. Consider the following statements for vectors u, v, w, and all scalars c.
br br br br br br br
br br
br
br
br br br br br br br br br br br br br



a. u · v = v · u br br br br br br



b. u · (v + w) = u · v + u · w
br br br br br br br br br br br br



c. (cu) · v = c(u · v) br br br br br br



d. u · u ≥ 0 and u · u = 0 if and inly if u = 0
br br br br br b r br br br br br br br br br br br




30. Find a value of k so that the angle between the line 4x + ky = 20 and the line 2x – 3y = –6 is 45°.
br br br br br br br br br br br br br br br br br br br br br br br br br br




31. Find the orthogonal projection of v = [–1, 2, 1] onto the xz-plane.
br br br br br br br br br br br br




32. Show that the quadrilateral with vertices A = (–3, 5, 6), B = (1, –5, 7), C = (8, –3, –1) and D = (4, 7, –2) is a square.
br br br br br br br br br br br br br br br br br br br br br br br br br br br br br




33. If a = [1, –2, 3], b = [4, 0, 1], c = [2, 1, –3], compute 2a – 3b + 4c.
br br br br br br br br br br br br br br br br br br br br br




3
that is perpendicular to the plane 2x – 3y + 7z –
br

34. Find the vector parametric equation of the line in
br br br br br br br br br br br br br br br br br br br br




4 = 0 and which passes through the point P = (l, –5, 7).
br br br br br br br br br br br br br br




35. Find all values of k such that d(a, b) = 6, where a = [2, k, 1, –4] and b = [3, –1, 6, –3].
br br br br br br br br br br br br br br br br br br br br br br br br




36. Show that if a vector v is orthogonal to two noncollinear vectors in a plane P, then v is orthogonal to every vector in
br br br br br br br br br br br br br br br br br br br br br br br



P.

37. Final all solutions of 7x = 1 in br br br br br br br br , or show that there are no solutions.
br br br br br br br




38. Let u1 and u2 be unit vectors, and let the angle between them be
br
br
br
br
br br br br br br br br br b r




b r radians. What is the area of the parallelogram whose diagonals are d1 = 2u1 – u2 and d2 = 4u1 –5u2?
br br br br br br br br br br br
br
br
br
br
br
br
br
br
br




Copyright Cengage Learning. Powered by Cognero.
br br br br br Page 3 br

, 39. Solve for the vector x in terms of a and b: 2x – a = 3b = 2(a + b) – (x – b).
br br br br br br br br br br br br br br br br br br br br br br br




40. Given p = [1, –2, 1], q = [4, –4, 7], find: br br br br br br br br br br br



a. p · q br br



b. ||p - q|| br br



c. projqp
d. the cosine of the angle between p and q
br br br br br br br br




3
in the opposite direction to v = [1, 2, –2].
br

41. Find a unit vector in br br br br br br br br br br br br br br




42. Let ABCDEF be a regular hexagon whose sides are of length 5. If
br br br br br br br br br br br br br = a and
br br br br br = b, find the projection of
br br br br br br




along a.
br br




43. Find a vector of length br br br br br that is orthogonal to both a = [2, 1, –3] and b = [1, –2, 1].
br br br br br br br br br br br br br br br br




44. Suppose that the dot product of two vectors u and v in br br br br br br br br br br br br


3 br

were defined as the product of the lengths of the vectors. Which (if any) of the following statements would be true for
br br br br br br br br br br br br br br br br br br br br br br




all vectors u, v, w, and all scalars c?
br br br br br br br br



a. u·v = v·u br br



b. u· (v + w) = u·v + u·w
br br br br br br br



c. c(u) ·v = c(u·v) br br br



d. u·u ≥ 0 and u·u = 0 if and only if u = 0
br br br b r br br br br br br br br br




Indicate the answer choice that best completes the statement or answers the question.
br br br br br br br br br br br br




2
45. Find the normal form of the equation of the line passing through point (2,3) and having a slope of 4 in
br br br br br br br br br br br br br br br br br br br br br ?
a.
b.
c.
d.

46. A set of forces br , br , br br br br




acts on an object. What is the resultant force (in vector form)?
br br br br br br br br br br br br



a.
b.
c.
d.

47. The vector form of the equation of the line in
br br br br br br br br br br br through P = (2, 0, – br br br br br




3) and parallel to the line with parametric equations:
br br br br br br br br




is



Copyright Cengage Learning. Powered by Cognero.
br br br br br Page 4 br