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Work Problem 1 a) Given the vectors in R3 v, = (11 -3), v,= ( 1 -3 1), v3=(-3 1 1) Using the system of linear equations determine whether the given vectors are linearly independent. b) Determine whether given vectors P,(t) = 21-t, p2(t) =²-3, p,(t)= t in P2 are linearly independent.

Work Problem 1 a) Given the vectors in R3 v, = (11 -3), v,= ( 1 -3 1), v3=(-3 1 1) Using the system of linear equations determine whether the given vectors are linearly independent. b) Determine whether given vectors P,(t) = 21-t, p2(t) =²-3, p,(t)= t in P2 are linearly independent.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section: Chapter Questions
Problem 14RQ
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Work Problem 1 a) Given the vectors in R3 v, = (11 -3), v,= ( 1 -3 1), v3=(-3 1 1) Using the system of linear equations determine whether the given vectors are linearly independent. b) Determine whether given vectors P,(t) = 21-t, p2(t) =-3, p3(t)= t in P2 are %3! linearly independent. Work Problem 3 ( a) Consider the set S= {+1, t+t, t+ 1}. Detrmine whether p(t) = 3t-5t+3 belongs to span S. b) Determine whether {t + 1, -t, t+1} is a spanning set.
Transcribed Image Text:Work Problem 1 a) Given the vectors in R3 v, = (11 -3), v,= ( 1 -3 1), v3=(-3 1 1) Using the system of linear equations determine whether the given vectors are linearly independent. b) Determine whether given vectors P,(t) = 21-t, p2(t) =-3, p3(t)= t in P2 are %3! linearly independent. Work Problem 3 ( a) Consider the set S= {+1, t+t, t+ 1}. Detrmine whether p(t) = 3t-5t+3 belongs to span S. b) Determine whether {t + 1, -t, t+1} is a spanning set.
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