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For each of the following subsets of R", determine whether it is a subspace of R" or not a) S = {(x₁, x2, x3) € R³|2x₁-3x₂ + x3 = 0} E b) Q = {(x₁, x2, x3, x4) € R¹ | x₁ = 3x3 and x₂ = 4x4 }

For each of the following subsets of R", determine whether it is a subspace of R" or not a) S = {(x₁, x2, x3) € R³|2x₁-3x₂ + x3 = 0} E b) Q = {(x₁, x2, x3, x4) € R¹ | x₁ = 3x3 and x₂ = 4x4 }

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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For each of the following subsets of R", determine whether it is a subspace of R" or not a) S = {(x₁, X2, X3) € R³|2x₁-3x₂ + x3 = 0} E b) Q = {(x₁, x2, x3, x4) E R¹ | x₁ = 3x3 and x₂ = 4x4}
Transcribed Image Text:For each of the following subsets of R", determine whether it is a subspace of R" or not a) S = {(x₁, X2, X3) € R³|2x₁-3x₂ + x3 = 0} E b) Q = {(x₁, x2, x3, x4) E R¹ | x₁ = 3x3 and x₂ = 4x4}
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