Let W be a subspace of Rn with an orthogonal basis{w1,..., wp}, and let {v1,..., v4} be an orthogonal basis forw+.a. Explain why {w1,.'p,V1, · . . ,V4} is an orthogonalset.b. Explain why the set in part (a) spans R".c. Show that dim W + dim W+ = n.

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Answered: Let W be a subspace of Rn with an…

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 a subspace of Rn with an orthogonal basis {w1,..., wp}, and let {v1,..., v4} be an orthogonal basis for w+. a. Explain why {w1,. 'p,V1, · . . , V4} is an orthogonal set. b. Explain why the set in part (a) spans R". c. Show that dim W + dim W+ = n.