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Consider the following functions. f1(x) = 0, f2(x) = x, f3(x) = ex g(x) = c1f1(x) + c2f2(x) + c3f3(x) Solve for c1, c2, and c3 so that g(x) = 0 on the interval (−[infinity], [infinity]). If a nontrivial solution exists, state it. (If only the trivial solution exists, enter the trivial solution {0, 0, 0}.) {c1, c2, c3} =

Respuesta :

LammettHash

There are infinitely many solutions for any choice of [tex]c_1[/tex] and [tex]c_2=c_3=0[/tex].

[tex]x[/tex] and [tex]e^x[/tex] are linearly independent and the only way to get [tex]c_2f_2+c_3f_3=0[/tex] is to choose [tex]c_2=c_3=0[/tex].

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