Show that every basis for R n must contain exactly n vectors. Let S = {v 1
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Show that every basis for Rn must contain exactly n vectors.
Let S = {v1,...,vk} be a set of k vectors in Rn, with k > n. Use a theorem from Chapter 1 to explain why S cannot be a basis for Rn.
Data from in Theorem 4
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If a set S = {₁,..., Vps in R" contains the zero vector, then the set is linearly dependent. PROOF By renumbering the vectors, we may suppose v₁ = 0. Then the equation 1v₁ + 0v₂ + + Ovp = 0 shows that S is linearly dependent.
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Let A be the n k matrix v 1 v k Since A has fewer rows than columns rows t...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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