2. A linearly independent set ({V₁,..., Vk) in R" can be extended to a basis for R". One way to do this is to create A = [v₁ Vk e₁en], with e₁, ..., e, the columns of the identity matrix. The columns containing the leading 1's in the RREF of A correspond to the columns of A needed to create a basis for R". Use this method to extend the following vectors to a basis for R³: V₁ = -7 -5 V2 = 9 4 1 6 V3 = 7 -8

2. A linearly independent set ({V₁,..., Vk) in R" can be extended to a basis for R". One way to do this is to create A = [v₁ Vk e₁en], with e₁, ..., e, the columns of the identity matrix. The columns containing the leading 1's in the RREF of A correspond to the columns of A needed to create a basis for R". Use this method to extend the following vectors to a basis for R³: V₁ = -7 -5 V2 = 9 4 1 6 V3 = 7 -8

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter7: Distance And Approximation

Section7.2: Norms And Distance Functions

Problem 33EQ

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