Let W and W, be two subspaces of a finite dimensional vector space V over a field F.1. Show that W1n W2 is a vector subspace of V, but that W1 U W2 need not be a vector subspace ingeneral.2. Show thatdim(W1) + dim(W2) – dim(W1 n W2) = dim(W1 + W2),where W1 + W2 just denotes the span of W1 u W2 in V. (Hint: Apply the rank nullity theorem to the naturalmap Wi O W2 → V.)

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Answered: Let W1 and W2 be two subspaces of a…

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 W1 and W2 be two subspaces of a finite dimensional vector space V over a field F. 1. Show that W1n W2 is a vector subspace of V, but that W¡u W2 need not be a vector subspace in general.