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,...,bn), and the coordinate mapping x ↦ [x] B.
Given vectors u1,...,up, and w in V, show that w is a linear combination of u1,...,up if and only if [w]B is a linear combination of the coordinate vectors [u1]B,...,[up]B.
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By definition w is a linear combination of u 1 u p if and only if there exist ...View the full answer
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Related Book For
Linear Algebra And Its Applications
ISBN: 9781292351216
6th Global Edition
Authors: David Lay, Steven Lay, Judi McDonald
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