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F. Let a = (a1, a2, ., am) E R" where ||a|| #0 and let beR. Let SC R" where S = {(x1, x2, ..., In) € R" : a1x1 + azx2+ ... + a„&n = b} %3D Show that the shortest distance from ở = (0,0,0, ...,0) € R" to the set S is . Hint: Let x = (r1, 82, ..., Tn) E S. We wan to minimize ||x - || subject to a1x1+ a2x2 +... + a„xn = b Let f(r1, 12, ., Tn) = |(x1, 2, .., In)F and g(x1, x2, ..., Im) = a,X1+a2®2+.+a„In-b %3D %3D and apply Lagrange Multiplier.

F. Let a = (a1, a2, ., am) E R" where ||a|| #0 and let beR. Let SC R" where S = {(x1, x2, ..., In) € R" : a1x1 + azx2+ ... + a„&n = b} %3D Show that the shortest distance from ở = (0,0,0, ...,0) € R" to the set S is . Hint: Let x = (r1, 82, ..., Tn) E S. We wan to minimize ||x - || subject to a1x1+ a2x2 +... + a„xn = b Let f(r1, 12, ., Tn) = |(x1, 2, .., In)F and g(x1, x2, ..., Im) = a,X1+a2®2+.+a„In-b %3D %3D and apply Lagrange Multiplier.

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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Answer the given problem below.

F. Let a = (a1, a2, ., am) E R" where ||a|| # 0 and let b E R. Let SC R" where .... S = {(x1, x2, .., In) E R" : a11+ a2x2+ + a,In = b} ... Show that the shortest distance from 0 = (0,0,0,., 0) E R" to the set S is b. Tla|| .... Hint: Let x = (r1, x2, ..., an) E S. We wan to minimize ||x - ||x – ở|| subject to a1x1 + a2x2 + ... 9 = "x"D + Let f(x1, x2, ., xn) = (*1, x2, ... Xn)||? and g(x1, 2,..., "n) = a1x1+azx2+..+a,&n-b and apply Lagrange Multiplier. %3D %3D
Transcribed Image Text:F. Let a = (a1, a2, ., am) E R" where ||a|| # 0 and let b E R. Let SC R" where .... S = {(x1, x2, .., In) E R" : a11+ a2x2+ + a,In = b} ... Show that the shortest distance from 0 = (0,0,0,., 0) E R" to the set S is b. Tla|| .... Hint: Let x = (r1, x2, ..., an) E S. We wan to minimize ||x - ||x – ở|| subject to a1x1 + a2x2 + ... 9 = "x"D + Let f(x1, x2, ., xn) = (*1, x2, ... Xn)||? and g(x1, 2,..., "n) = a1x1+azx2+..+a,&n-b and apply Lagrange Multiplier. %3D %3D
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