Concern a vector space V, a basis B = {b 1 ,...,b n ), and the coordinate

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Concern a vector space V, a basis B = {b₁,...,b_n), and the coordinate mapping x ↦ [x] _B.

Show that a subset {u₁,...,u_p} in V is linearly independent if and only if the set of coordinate vectors {[u₁]_B,...,[U_p]_B} is linearly independent in Rⁿ.

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Linear Algebra And Its Applications

ISBN: 9781292351216

6th Global Edition

Authors: David Lay, Steven Lay, Judi McDonald

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Question Posted: May 03, 2023 04:41 AM

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Concern a vector space V, a basis B = {b 1 ,...,b n ), and the coordinate

Question:

+ Cpup = 0 The zero vector in V [C₁u₁ ++Cpup lg = [0] The zero vector in R" B B

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Since the coordinate mapping is onetoone the followi...View the full answer

Linear Algebra And Its Applications

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