(a) (3) Let V be a vector space over some field F Let W be a subspace of a vector space V. Suppose x, y € V are not in W. at if x € span (W, y) then y € span(W,x) (b) Give an example of a vector space V, a subspace W≤ V, and vectors x, y € V such that x e span(W,y) but y & span(W, x)

(a) (3) Let V be a vector space over some field F Let W be a subspace of a vector space V. Suppose x, y € V are not in W. at if x € span (W, y) then y € span(W,x) (b) Give an example of a vector space V, a subspace W≤ V, and vectors x, y € V such that x e span(W,y) but y & span(W, x)

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter5: Inner Product Spaces

Section5.CR: Review Exercises

Problem 54CR: Let V be an two dimensional subspace of R4 spanned by (0,1,0,1) and (0,2,0,0). Write the vector...

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I just need a simple explanation for the first question. Thank you.

(a)
(3) Let V be a vector space over some field F
Let W be a subspace of a vector space V. Suppose x, y € V are not in W.
at if x = span (W, y) then y ≤ span(W,x)
(b)
Give an example of a vector space V, a subspace W ≤ V, and vectors x, y € V
such that x e span(W,y) but y & span(W, x)

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