1. Consider subsets W of a vector space V: = 0}; (a) V = R³, W = {[₁,2,3]|2x12x2 + x3 = (b) V=R³, W = {[a-b, 3b+2a, a-b] | a, b = R}; (c) V = R4, W = {[₁, 2, 3, 4] | 21-2a2+3+4= 5}. In each case determine if the given subset W of a vector space V is a su when W is a subspace of V, find a basis and the dimension of W. Just.
1. Consider subsets W of a vector space V: = 0}; (a) V = R³, W = {[₁,2,3]|2x12x2 + x3 = (b) V=R³, W = {[a-b, 3b+2a, a-b] | a, b = R}; (c) V = R4, W = {[₁, 2, 3, 4] | 21-2a2+3+4= 5}. In each case determine if the given subset W of a vector space V is a su when W is a subspace of V, find a basis and the dimension of W. Just.
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter4: Vector Spaces
Section4.4: Spanning Sets And Linear Independence
Problem 74E: Let u, v, and w be any three vectors from a vector space V. Determine whether the set of vectors...
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![1.
Consider subsets W of a vector space V:
(a) V = R³, W = {[#1, #2, #3] | − 2x1 − 2x2₂ + x3 = 0};
(b) V = R³, W = {[ab, 3b+2a, a - b] | a, b = R};
(c) V = R¹, W = {[1, 22, 23, ₁] | − 2x₁ − 2x2 + x3 +2₁ = 5}.
In each case determine if the given subset W of a vector space V is a subspace. In cases
when W is a subspace of V, find a basis and the dimension of W. Justify every step of
your answer.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F655e5d67-ab19-404c-b883-3aa3c693f6a1%2Ffa15e706-c41e-49d7-b212-fbecfbfcf7d1%2Fgdsuacc_processed.png&w=3840&q=75)
Transcribed Image Text:1.
Consider subsets W of a vector space V:
(a) V = R³, W = {[#1, #2, #3] | − 2x1 − 2x2₂ + x3 = 0};
(b) V = R³, W = {[ab, 3b+2a, a - b] | a, b = R};
(c) V = R¹, W = {[1, 22, 23, ₁] | − 2x₁ − 2x2 + x3 +2₁ = 5}.
In each case determine if the given subset W of a vector space V is a subspace. In cases
when W is a subspace of V, find a basis and the dimension of W. Justify every step of
your answer.
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