Let W be a subspace spanned by the u's, and write y as the sum of a vector in W and a vector orthogonal to W.y =u =2u2 =u3 =- 1...y =D

Given W be a subspace spanned by the u's, We have to write y as the sum of a vector in W and a…

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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 be the subspace spanned by u₁ and u₂, and write y as the sum of a vector in W and a vector orthogonal to W y = - 6 5 7 1 , U₁ = 1 1, ₂ = 1 1 3 - 2 The sum is y = y + z, where y = is in W and z= (Simplify your answers.) is orthogonal to W. ***
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Find the distance from the point x = (1, 5, -4) of R to the subspace W consisting of all vectors of the form (a, a, b).
Please provide a solution using the answer key I have attached below.

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Let W be a subspace spanned by the u's, and write y as the sum of a vector in W and a vector orthogonal to W. - 1 - 1 2 y = u2 = uz = 2 1 - 4