F. Let a = :(a1, a2, ..., an) E R" where ||a|| +0 and let be R. Let SC R" where S = {(x1, x2, .., Xn) E R" : a1x1+ a2X2+ .. + anXn = b} =(0,0,0, ..., 0) E R" to the set S is ||a|| · Show that the shortest distance from Hint: Let x = (x1, x2, ..., xn) E S. We wan to minimize ||x – || subject to a1x1 + a2x2+ + anxn = b ... Let f(x1, x2, .., xn) = }||(x1, x2, .., Xn)||² and g(x1, x2, ..., Xn) = a1X1+azx2+...+an&n=b 2:.... and apply Lagrange Multiplier.
F. Let a = :(a1, a2, ..., an) E R" where ||a|| +0 and let be R. Let SC R" where S = {(x1, x2, .., Xn) E R" : a1x1+ a2X2+ .. + anXn = b} =(0,0,0, ..., 0) E R" to the set S is ||a|| · Show that the shortest distance from Hint: Let x = (x1, x2, ..., xn) E S. We wan to minimize ||x – || subject to a1x1 + a2x2+ + anxn = b ... Let f(x1, x2, .., xn) = }||(x1, x2, .., Xn)||² and g(x1, x2, ..., Xn) = a1X1+azx2+...+an&n=b 2:.... and apply Lagrange Multiplier.
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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Please answer
Transcribed Image Text:F.
Let a = (a1, a2,
.., an) E R" where ||a|| + 0 and let b e R. Let SC R" where
S = {(x1, x2, ..., Xn) E R" : a1X1+ a2X2+ ... + anxn = b}
Show that the shortest distance from 0 = (0,0,0, ..., 0) E R" to the set S is
||a||
Hint: Let x =
(x1, x2, ..., xn) E S. We wan to minimize
||x – ||
subject to
a1X1+ a2x2 +
+ anxn = 6
...
Let f(x1, x2,.., Xn)
|(*1, x2, ..., xn)||² and g(x1, x2, ..., Xn) = a1x1+a2x2+...+anXn–b
....
and apply Lagrange Multiplier.
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