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(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)

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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(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)
Transcribed Image Text:(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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