5. Suppose us v and w are linearly independent vectors. Prove that (i) и+у - 2w, и — v — w, и+ w are linearly independent. (ii) и + у-Зw, и + Зу— и, и + w are linearly independent.

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.3: Spanning Sets And Linear Independence
Problem 21EQ
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5.
Suppose us v and w are linearly independent vectors. Prove that
(i)
и+у - 2w, и — v — w, и+ w
are linearly independent.
(ii) и + у-Зw, и + Зу— и, и + w
are linearly independent.
Transcribed Image Text:5. Suppose us v and w are linearly independent vectors. Prove that (i) и+у - 2w, и — v — w, и+ w are linearly independent. (ii) и + у-Зw, и + Зу— и, и + w are linearly independent.
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