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Let n ≥ 3. Identify which of the following subsets are subspaces of the R-vecto: space R. Give brief justifications for your answers. (i) V₁ = {(x₁,x2,...,xn) € Rn | x₁ ≥ 0}. (ii) V₂ = {(x1,x2,...,xn) € Rn | x₁ + 3x2 = x3}. 2 (iii) V3 = {(x₁,x2,...,xn) € R¹ | x² +9x²/2 x}}. (iv) V₁ = {(x₁,x2,...,xn) € Rn | x₁x2 = 0}. (v) V5 = {(x₁,x2,...,xn) € Rª | x₂ € Q}. (vi) V6 = {(x₁,x2,...,xn) € R¹ | πxX2 € Q}. solve all six equations plz. Thx in advance! =

Let n ≥ 3. Identify which of the following subsets are subspaces of the R-vecto: space R. Give brief justifications for your answers. (i) V₁ = {(x₁,x2,...,xn) € Rn | x₁ ≥ 0}. (ii) V₂ = {(x1,x2,...,xn) € Rn | x₁ + 3x2 = x3}. 2 (iii) V3 = {(x₁,x2,...,xn) € R¹ | x² +9x²/2 x}}. (iv) V₁ = {(x₁,x2,...,xn) € Rn | x₁x2 = 0}. (v) V5 = {(x₁,x2,...,xn) € Rª | x₂ € Q}. (vi) V6 = {(x₁,x2,...,xn) € R¹ | πxX2 € Q}. solve all six equations plz. Thx in advance! =

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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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 = {(x₁,x2,...,xn) € R¹ | x₁ ≥ 0}. (ii) V₂ = {(x₁,x2,...,xn) (iii) V3 = {(x₁,x2,...,xn) (iv) V₁ = {(₁, 2,...,xn) € R¹ | x₁ + 3x2 = x3}. x1 = R¹ | x² + 9x² = x²}. = R² | x1x2 = 0}. € (v) V5 = {(x1,x2,...,xn) (vi) V6 = {(x1,x2,...,xn) = R¹ | πX₂ € Q}. € solve all six equations plz. Thx in advance! = R | x₂ ≤ Q}. x2
Transcribed Image Text: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 = {(x₁,x2,...,xn) € R¹ | x₁ ≥ 0}. (ii) V₂ = {(x₁,x2,...,xn) (iii) V3 = {(x₁,x2,...,xn) (iv) V₁ = {(₁, 2,...,xn) € R¹ | x₁ + 3x2 = x3}. x1 = R¹ | x² + 9x² = x²}. = R² | x1x2 = 0}. € (v) V5 = {(x1,x2,...,xn) (vi) V6 = {(x1,x2,...,xn) = R¹ | πX₂ € Q}. € solve all six equations plz. Thx in advance! = R | x₂ ≤ Q}. x2
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