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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*.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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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