Show that every basis for R n must contain exactly n vectors Let S v 1 , ,v k be a set of k vectors in R n , with k n Data from in Theorem If a set S , , Vps in R contains the zero vector, then the set is linearly dependent PROOF By renumbering the vectors, we may suppose v 0 Then the equation 1v 0...

Let A be the n k matrix v 1 v k Since A has fewer columns than rows there cannot be a ...

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,...,v_k} be a set of k vectors in Rⁿ, with k n.

Data from in Theorem

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Linear Algebra And Its Applications

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6th Global Edition

Authors: David Lay, Steven Lay, Judi McDonald

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Show that every basis for R n must contain exactly n vectors. Let S = {v 1

Question:

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 columns than rows there cannot be a ...View the full answer

Linear Algebra And Its Applications

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