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(iv) V₁ = {(₁, ₂,..., In) € R¹ | I₁I₂ = 0}. (v) V₁ = {(₁, ₂,..., n) = R¹ | 1₂ € Q}. (vi) V6 = {(₁, 2,..., In) = R¹ | x₂ € Q}.

(iv) V₁ = {(₁, ₂,..., In) € R¹ | I₁I₂ = 0}. (v) V₁ = {(₁, ₂,..., n) = R¹ | 1₂ € Q}. (vi) V6 = {(₁, 2,..., In) = R¹ | x₂ € Q}.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 22E
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section (iv)~(vi)

Problem 4. Let n ≥ 3. Identify which of the following subsets are subspaces of the R-vector space R". Give brief justifications for your answers. (i) V₁ = {(₁, 2,...,xn) € R₂ | ₁ ≥ 0}. (ii) V₂ = {(₁, 2,..., In) € R¹ | 1₁ + 3x₂ = x3}. (iii) V3 = {(x1, x2,...,xn) € R¹ | x² + 9x² = x²}. (iv) V₁ = {(₁, 2,...,xn) € R¹ | I₁*₂ = 0}. 2,...,xn) € R¹ | 1₂ € Q}. (v) V5 = {(₁, (vi) V6 = {(₁, 2,..., In) € R¹ | TX₂ € Q}.
Transcribed Image Text:Problem 4. Let n ≥ 3. Identify which of the following subsets are subspaces of the R-vector space R". Give brief justifications for your answers. (i) V₁ = {(₁, 2,...,xn) € R₂ | ₁ ≥ 0}. (ii) V₂ = {(₁, 2,..., In) € R¹ | 1₁ + 3x₂ = x3}. (iii) V3 = {(x1, x2,...,xn) € R¹ | x² + 9x² = x²}. (iv) V₁ = {(₁, 2,...,xn) € R¹ | I₁*₂ = 0}. 2,...,xn) € R¹ | 1₂ € Q}. (v) V5 = {(₁, (vi) V6 = {(₁, 2,..., In) € R¹ | TX₂ € Q}.
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