4. your answer. Determine whether each of the following sets is a subspace of R³ and justify (a) W = {(₁, 12, 13) € R³ : x₁ + x3 = 2x₂, 1 — 13 = 31₂}. (b) W = {(₁, 72, 73) € R³ : x₂ + 1 = ₁ + €²2}. (c) W = {(₁, 22, 23) € R³: x²+x=0}.
4. your answer. Determine whether each of the following sets is a subspace of R³ and justify (a) W = {(₁, 12, 13) € R³ : x₁ + x3 = 2x₂, 1 — 13 = 31₂}. (b) W = {(₁, 72, 73) € R³ : x₂ + 1 = ₁ + €²2}. (c) W = {(₁, 22, 23) € R³: x²+x=0}.
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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Transcribed Image Text:Determine whether each of the following sets is a subspace of R³ and justify
4.
your answer.
(a) W = {(₁, 2, 3) ≤ R³ : x₁ + x3 = 2x2, 2₁-23 = 3x₂}.
(b) W = {(₁, 22, 23) € R³ : x3 + 1 = x₁ + €²2}.
(c) W = {(1, 2, 3) = R³ : x² + x² = 0}.
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