1. Show that {1, (x - 1), (x - 1)(x - 2)} are linearly independent and are a spanning set. Note that p(x) = a +bx+cr² € W if and only if p(1) = a +b+c= 0, then using this to show that W is closed under addition and scalar multiplication.

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.4: The Singular Value Decomposition
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1. Show that {1, (x - 1), (x - 1)(x - 2)} are linearly independent and are a spanning set.
Note that p(x) = a +bx+cr² € W if and only if p(1) = a +b+c= 0, then using this to
show that W is closed under addition and scalar multiplication.
Transcribed Image Text:1. Show that {1, (x - 1), (x - 1)(x - 2)} are linearly independent and are a spanning set. Note that p(x) = a +bx+cr² € W if and only if p(1) = a +b+c= 0, then using this to show that W is closed under addition and scalar multiplication.
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