1) We write vectors horizontally for this problem. Let U be the subspace of IRS defined by U = {(x1,x2, X3, X4, Xs)|X1, X2, X3, X4, X5 € R, x1 = 3x2 and x3 = 7x4}. a) Find a basis of U b) Extend the basis in part (a) to a basis of R c) Find a subspace W of R$ such that RS = U OW.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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1) We write vectors horizontally for this problem. Let U be the subspace of RS defined
by
U = {(x1, X2, X3, X4, x3)|X1, X2, X3, X4, X5 E R, x, = 3x, and x3 = 7x4}.
a) Find a basis of U
b) Extend the basis in part (a) to a basis of RS
c) Find a subspace W of R5 such that R5 = U OW.
Transcribed Image Text:1) We write vectors horizontally for this problem. Let U be the subspace of RS defined by U = {(x1, X2, X3, X4, x3)|X1, X2, X3, X4, X5 E R, x, = 3x, and x3 = 7x4}. a) Find a basis of U b) Extend the basis in part (a) to a basis of RS c) Find a subspace W of R5 such that R5 = U OW.
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