Prove directly that the functions f1.x/ 1; f2.x/ D x; and
Chapter , Problem 27(choose chapter or problem)
Prove directly that the functions f1.x/ 1; f2.x/ D x; and f3.x/ D x2 are linearly independent on the whole real line. (Suggestion: Assume that c1 C c2x C c3x2 D 0. Differentiate this equation twice, and conclude from the equations you get that c1 D c2 D c3 D 0.)
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