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Let a = (a1, a2, ..., an) E R" where ||a|| 70 and let b e R. Let SC R" where S = {(x1, x2, ..., Xn) E R" : a1x1 + a2x2 +... + anXn Show that the shortest distance from 0 = (0,0, 0, ...,0) e R" to the set S is - Hint: Let x = (x1, x2, ..., xn) E S. We wan to minimize ||x – || subject to a1X1+ a2x2 + ... + anxn = b Let f(x1, x2, ..., n) = }||("1, x2, ..., n) ||? and g(x1, x2, ., n) = a1x1+a2X2+...+anXn-6 and apply Lagrange Multiplier.

Let a = (a1, a2, ..., an) E R" where ||a|| 70 and let b e R. Let SC R" where S = {(x1, x2, ..., Xn) E R" : a1x1 + a2x2 +... + anXn Show that the shortest distance from 0 = (0,0, 0, ...,0) e R" to the set S is - Hint: Let x = (x1, x2, ..., xn) E S. We wan to minimize ||x – || subject to a1X1+ a2x2 + ... + anxn = b Let f(x1, x2, ..., n) = }||("1, x2, ..., n) ||? and g(x1, x2, ., n) = a1x1+a2X2+...+anXn-6 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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Let a = (a1, a2, ..., an) E R" where ||a|| # 0 and let b e R. Let S C R" where {(x1, x2, ..., xn) E R" : a1x1+ a2x2 + ... + anXn = b} S = 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 A2X2 + ... + anXn = b Let f(x1, x2, ..., n) = }||(x1, x2, ..., n)||? and g(x1, x2, ., n) = a1x1+a2x2+..+a„¤n=b and apply Lagrange Multiplier.
Transcribed Image Text:Let a = (a1, a2, ..., an) E R" where ||a|| # 0 and let b e R. Let S C R" where {(x1, x2, ..., xn) E R" : a1x1+ a2x2 + ... + anXn = b} S = 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 A2X2 + ... + anXn = b Let f(x1, x2, ..., n) = }||(x1, x2, ..., n)||? and g(x1, x2, ., n) = a1x1+a2x2+..+a„¤n=b and apply Lagrange Multiplier.
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