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a az that satisfy a, -a, = a, – a,. az 3. In R", let Wbe the subset of all vectors v = a4 a) Show that W is a subspace of R*.

a az that satisfy a, -a, = a, – a,. az 3. In R", let Wbe the subset of all vectors v = a4 a) Show that W is a subspace of R*.

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
Section2.3: Spanning Sets And Linear Independence
Problem 21EQ
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a, az 3. In R, let W be the subset of all vectors v= that satisfy a, -a, = a, – a,. az a4 a) Show that W is a subspace of R*. 1 1 b) Show that S=. spans W. c) Find a subset of S that is a basis for W. d) Express v= 4 as a linear combination of the basis obtained in part (c). 6.
Transcribed Image Text:a, az 3. In R, let W be the subset of all vectors v= that satisfy a, -a, = a, – a,. az a4 a) Show that W is a subspace of R*. 1 1 b) Show that S=. spans W. c) Find a subset of S that is a basis for W. d) Express v= 4 as a linear combination of the basis obtained in part (c). 6.
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