4.Let W = Span{v1, v2} with ui =2and v2 =2(a) Show that {õ1, 02} is an orthogonal basis for W.(b) Construct an orthonormal basis {ū1, ū2} for W.(c) Construct the projection matrix P = UUT such that projw y = Pj.-6(d) Using your result from part (c), write the vector j =as the sum of a vector in W9.6.and a vector in W-.

Please find the answers in next steps we have answers first three subparts only as per company…

Answered: 国… 4. Let W = Span{v1, v2} with ui = 2…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

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21 U2 = -2] Let uj = u2 1 and y = 2 [3. and W= Span{u1,U2}. (a) Find an orthogonal basis for W. (b) Find the closest point in W to y. (c) What is the shortest distance between y and W?

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国… 4. Let W = Span{v1, v2} with ui = 2 and v2 = 2 (a) Show that {õ1, 02} is an orthogonal basis for W. (b) Construct an orthonormal basis {ū1, ū2} for W. (c) Construct the projection matrix P = UUT such that projw j = Pj.