According to Theorem 12, a linearly independent set {v 1 ,...,v k in R n can be

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According to Theorem 12, a linearly independent set {v1,...,vk in Rn can be expanded to a basis for Rn. One way to do this is to create A = [v1 ... vk e1 ... en], with e1,...,en  the columns of the identity matrix; the pivot columns of A form a basis for Rn

a. Use the method described to extend the following vectors to a basis for R5:

b. Explain why the method works in general: Why are the original vectors V,..., Vk included in the basis found for Col A? Why is Col A = Rn?


Data from in Theorem 12

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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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