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Do the following. Considering the subspace W of R^4 , which has as its basis the set B = 2 (a) Explicitly describe the orthogonal complement W+ of W and give a basis and the dimension of this subspace; (b) Consider the following FACT from theory (theorem): If v1,v2, .. , vr is an orthogonal basis of a subspace W of R" and v €R" then the vector projection projw (v) of v onto W is given by : projw (v) = projui (v) + projuz(v) +...+ proju, (v). It is further proven that this is the vector of W closest to the vector v. 2 Given the result above, find the vector of W closest to 1 E R'. v = 3

Do the following. Considering the subspace W of R^4 , which has as its basis the set B = 2 (a) Explicitly describe the orthogonal complement W+ of W and give a basis and the dimension of this subspace; (b) Consider the following FACT from theory (theorem): If v1,v2, .. , vr is an orthogonal basis of a subspace W of R" and v €R" then the vector projection projw (v) of v onto W is given by : projw (v) = projui (v) + projuz(v) +...+ proju, (v). It is further proven that this is the vector of W closest to the vector v. 2 Given the result above, find the vector of W closest to 1 E R'. v = 3

Advanced Engineering Mathematics
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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Do the following. Considering the subspace W of R^4 , which has as its basis the set B = 2 (a) Explicitly describe the orthogonal complement W+ of W and give a basis and the dimension of this subspace; (b) Consider the following FACT from theory (theorem): If v1,v2, .. , vr is an orthogonal basis of a subspace W of R" and v €R" then the vector projection projw (v) of v onto W is given by : projw (v) = proju, (v) + projuz(v) +...+ projo, (v). It is further proven that this is the vector of W closest to the vector v. Given the result above, find the vector of W closest to 1 E R'. v = 3
Transcribed Image Text:Do the following. Considering the subspace W of R^4 , which has as its basis the set B = 2 (a) Explicitly describe the orthogonal complement W+ of W and give a basis and the dimension of this subspace; (b) Consider the following FACT from theory (theorem): If v1,v2, .. , vr is an orthogonal basis of a subspace W of R" and v €R" then the vector projection projw (v) of v onto W is given by : projw (v) = proju, (v) + projuz(v) +...+ projo, (v). It is further proven that this is the vector of W closest to the vector v. Given the result above, find the vector of W closest to 1 E R'. v = 3
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