(a) Suppose V is a vector space of dimension d. Let S = {w1,w2, . . . ,wn} be a set of vectors fromV. Then show that S does not span V if n < d.(b) Let {w1,w2, . . . ,wn} be a basis of the finite dimensional vector space V. Let v be any nonzero vector in V. Show that there exists wi such that if we replace wi by v then we still have abasis (a) Suppose V is a vector space of dimension d. Let S = {w1, w2, . . . , wn}be a set of vectors fromV. Then show that S does not span V if n < d.(b) Let {w1, w2,wn} be a basis of the finite dimensional vector space V. Let v be any nonzero vector in V.Show that there exists wi such that if we replace wi by v then we still have abasis1

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Answered: tors fromV. Then show that S does not…

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tors fromV. Then show that S does not span Vif , wn} be a basis of the finite dimensional ve

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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Question

(a) Suppose V is a vector space of dimension d. Let S = {w1,w2, . . . ,wn} be a set of vectors from
V. Then show that S does not span V if n < d.

(b) Let {w1,w2, . . . ,wn} be a basis of the finite dimensional vector space V. Let v be any non
zero vector in V. Show that there exists wi such that if we replace wi by v then we still have a
basis

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