Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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section (i)~(iii)

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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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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