Linear Algebra: A Modern Introduction 5th Edition testbank by David Poole ISBN:978-8214013054 COMPLETE GUIDE ALL CHAPTERS COVERED 100% VERIFIED A+

Test Bank For
R R




Linear Algebra A Modern Introduction 5th Edition by David Poole 2026
R R R R R R R R R RR




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,Section 1.0 - 1.4 R R R




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



a. True
b. False

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



a. True
b. False

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



a. True
b. False

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

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




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.
R R R R R R R R R R R R R R R R R R R R R R



a. True
b. False

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



a. True
b. False

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



a. True
b. False


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

a. True
b. False

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

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




a. True
b. False

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



a. True
b. False




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




a. True
b. False

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



a. True
b. False

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



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
R R R R R R R R R R R R R R R R R R R R R R R R



in the message will be even.
R R R R R



a. True
b. False

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



a. True
b. False

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



a. True
b. False

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



a. True
b. False




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


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




a. 2
R



b. 4
R



c. 6
R



d. 8
R




Find the distance between the parallel lines.
R R R R R R R


20.
and
R R




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


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, 22. Find the distance between the planes R R R R R R R and R .

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



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




24. Simplify the following expressions: R R R



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



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




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




1, 1]. R




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




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 –
R R R R R R R R R R R R R R R R R R R R R R R R R R R R R



2y + 2z = –17?
R R R R R




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




R and R R as linear combinations of a and b.
R R R R R R




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



2 R

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



a. u · v = v · uR R R R R R



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



c. (cu) · v = c(u · v) R R R R R R



d. u · u ≥ 0 and u · u = 0 if and inly if u = 0
R R R R R R R R R R R R R R R R R




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




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




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.
R R R R R R R R R R R R R R R R R R R R R R R R R R R R R




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




3
34. Find the vector parametric equation of the line in that is perpendicular to the plane 2x – 3y + 7z –
R

R R R R R R R R R R R R R R R R R R R R




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




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




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
R R R R R R R R R R R R R R R R R R R R R R R



P.

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




38. Let u1 and u2 be unit vectors, and let the angle between them be
R
R
R
R
R R R R R R R R R R




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




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