Let \( W = \{ (a, 2b, b-a) : a, b \in \mathbb{R} \} \) be a subspace of \( \mathbb{R}^3 \).- Find an orthonormal basis for \( W \).- Find the distance from the point \( (5, 1, -2) \) of \( \mathbb{R}^3 \) to \( W \).

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Answered: Let W = {(a, 2b, b-a): a, b ER} be…

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 W = {(a, 2b, b-a): a, b ER} be subspace of R³. o Find an orthonormal basis for W. • Find the distance from the point (5, 1, -2) of R³ to W.