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Prove directly that the functions f1(x) = 1, f2(x) = x, and f3(x) = x² = x² are linearly independent on the whole real line. (Sug

Prove directly that the functions f1(x) = 1, f2(x) = x, and f3(x) = x² = x² are linearly independent on the whole real line. (Sug

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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27. Prove directly that the functions fi (x) = 1, f2(x) = x, and f3(x) = x² are linearly independent on the whole real line. (Sugges- tion: Assume that c1 + c2x + c3x² = 0. Differentiate this equation twice, and conclude from the equations you get that c1 = c2 = c3 = 0.)
Transcribed Image Text:27. Prove directly that the functions fi (x) = 1, f2(x) = x, and f3(x) = x² are linearly independent on the whole real line. (Sugges- tion: Assume that c1 + c2x + c3x² = 0. Differentiate this equation twice, and conclude from the equations you get that c1 = c2 = c3 = 0.)
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