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 isb.Tla||....Hint: Let x = (r1, x2, ..., an) E S. We wan to minimize||x -||x – ở||subject toa1x1 + a2x2 +...9 = "x"D +Let f(x1, x2, ., xn) = (*1, x2, ... Xn)||? and g(x1, 2,..., "n) = a1x1+azx2+..+a,&n-band apply Lagrange Multiplier.%3D%3D

Given that fx1,x2,...,xn=12x1,x2,...,xn2 gx1,x2,...,xn=a1x1+a2x2+...+anxn-b

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.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.2: Graphs Of Equations

Problem 68E

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