Consider the coordinate vectors-851[w]s-2, [als2. [B]s!!(a) Find w if S is the basis in {(3, 1, -4), (2, 5, 6), (1,4,8)}.w =|(?,?,?)(b) Find q if S is the basis in r +1, x² – 1, 2x - 1.[3(c) Find B if S is the basis in312? ?B =? ?220

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Answered: Consider the coordinate vectors 7 [5]…

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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10. In R3, let S be the set of vectors -1 1 S = {v1,V2, V3, V4} = 4 -3 -2 %3D -4 0. -4 Explain why S spans R³ but is not a basis for R3. Delete one of the vectors from S to form a new set of vectors, that is a basis for R3. a. b.
The prove that the vectors A,B and C form a basis. And decompose the vector D by basis vectors A, B and C. a = (3,1,2); b = (-4,3,-1), c = (2,3,4), d = (14,14,20)
2. Consider the following sets of vectors. Show that each set (i) contains the zero vector, (ii) is closed under addition and scalar multiplication. Then find a basis for each set and give the dimension. (a) W is the set of vectors of the form (3s, -2s, s). (b) W is the set of vectors of the form (t – 2, 0,6 – 3t). (c) H is the set of vectors of the form (2b, a, 3b) (d) H is the set of vectors of the form (-b+ 2c, b, 4c),
Let u = (1,3, 5) and v = (-4,3, –7) be vectors in R3. (a) Find u + v. (b) Express u in terms of the standard basis vectors in R3. (c) Find -3u.
Find the representation of (9, -2, -3) in each of the following ordered bases. Your answers should be vectors of the general form . a. Represent the vector (9, -2, -3) in terms of the ordered basis B = {i,j,k}. [(9,-2,-3)]B= b. Represent the vector (9, -2, -3) in terms of the ordered basis C = {3, e1, e2}. [(9,-2,-3)] c = c. Represent the vector (9, -2, -3) in terms of the ordered basis D= {-2, -1, e3}. [(9,-2,-3)]D =
Either find the coordinates of the vector relative to basis B, or find the original vector from the coordinates relative to basis B. (a) v = (3,5,10); B = {(1,0,−1), (2, 1, −1), (-2, 1,4)} for R³. (b) v = (13,54); B = {(1,0), (0, 1)} for R². (c) [v]B = (10,-1, 4); B = {(1,0,−1), (2, 1, −1), (−2, 1,4)} for R³.
Let {1, 2, 3, 4, 5, 6} be the standard basis in R6. Find the length of the vector = 3₁ - 22 - 2ě3 - 2ě4 – 2e5 - 3ē6. #
1. Vectors v1 = (1,1,1,1,0), v2 = (-1,1,0,0,0), v3 = (1,1,-1,-1,0), v4 = (0,0,2,-2,0) and v5 = (0,0,0,0,2) form an orthogonal basis for a of R5 and X = (-3, -2,5,1,-4). Find the coordinates of X with respect to the given basis.
: Let S = {v1, v2}, where v = standard vectors when added to the set S produces a basis for R? (6,-5, 7,-1) and v2 = (-12, 20, -28, 4). Which of the following combination of (A) v3 = (1, 0, 0, 0), v4 = (0, 0, 1, 0) and vs = (0, 0, 0, 1) (B) v3 = (1, 0, 0, 0), v4 = (0, 1, 0, 0) and vs = (0, 0, 0, 1) (C) v3 = (1, 0, 0, 0) and v4 = (0, 0, 0, 1) (D) v3 = (1, 0, 0, 0), v4 = (0, 1, 0, 0) and vs = (0. 0, 1, 0) (E)v3 = (1, 0, 0, 0) and v4 = (0, 1, 0, 0) (F) v3 = (1, 0, 0, 0) and v4 = (0, 0, 1, 0) (G) v3 = (0, 1, 0, 0) and v4 = (0, 0, 0, 1) %3D %3D (H) v3 = (0, 1, 0, 0), v4 = (0, 0, 1, 0) and vs = (0. 0, 0, 1) %3D

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Consider the coordinate vectors 7 [5] [w]s = -2, [als 2. [B]s: !! %3D %3D L5] (a) Find w if S is the basis in {(3, 1, –4), (2, 5, 6), (1,4, 8)}. w = (?,?,?) (b) Find q if S is the basis in r² + 1, x² – 1, 2x – 1. [3 (c) Find B if S is the basis in 3 12 ? ? %3D ? 220