Problem 1 (Basis and Dimension)LetX13€ R³ : x₁ + x2 + x3 = 0U = {( ²2 ) 0}:=x2X3be a subspace of R³.(a) Find a basis of U and determine the dimension.(b) Is one of the following families a basis of U? Jusitfy your answer.(i)(0)·()) - (0)·0)·())) - (Q)())(iii)

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Answered: Let U := (i) x1 {( x2 x3 be a subspace…

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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Let U := (i) x1 {( x2 x3 be a subspace of R³. (a) Find a basis of U and determine the dimension. (b) Is one of the following families a basis of U? Jusitfy your answer. € R³: x₁ + x₂ + x3 = 0 (0)·()) -(0)))) - (Q)-()) (iii) 1 2 (ii)