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2 (b) {(x1, x2) x = x²} CR² : (c) {(x1, x2, x3): x₁ = 2x2 + x3} CR³ X1

2 (b) {(x1, x2) x = x²} CR² : (c) {(x1, x2, x3): x₁ = 2x2 + x3} CR³ X1

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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1. Decide whether each of the following is a subspace of the indicated vector space.
Transcribed Image Text:1. Decide whether each of the following is a subspace of the indicated vector space.
(b) {(x₁,x₂): x² = x²} < R² (c) {(x1, x2, x3): x₁ = 2x2 + x3} CR³ x1
Transcribed Image Text:(b) {(x₁,x₂): x² = x²} < R² (c) {(x1, x2, x3): x₁ = 2x2 + x3} CR³ x1
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Step 1: Necessary and sufficient condition for a subset to form a subspace.

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