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Let W, and W2 be subspaces of a vector space V. Prove that V is the direct sum of W, and W2 if and only if each vector in V can be uniquely written as r1 + 2, where 1 E W1 and r2 E W2.

Let W, and W2 be subspaces of a vector space V. Prove that V is the direct sum of W, and W2 if and only if each vector in V can be uniquely written as r1 + 2, where 1 E W1 and r2 E W2.

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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Let W, and W2 be subspaces of a vector space V. Prove that V is the direct sum of W, and W2 if and only if each vector in V can be uniquely written as r1 + 2, where 1 E W1 and r2 E W2.
Transcribed Image Text:Let W, and W2 be subspaces of a vector space V. Prove that V is the direct sum of W, and W2 if and only if each vector in V can be uniquely written as r1 + 2, where 1 E W1 and r2 E W2.
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