Let f and g be functions defined by S() = e" and g(t) = e", where r # s. Prove that f and g are linearly independent in F(R, R). Hint: Suppose that ae" + be" = 0. Let t= 0 to obtain an equation involving a and b. Then differentiate ae" + be" = 0, and let t=0 to obtain a second equation involving a and b. Solve these equations for a and b.

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