Show that {e^x, e^(x+2)} are linearly independent

Question

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Let C1e^x + C2e^(x+2) = 0
for x = ln1: C1(1) + C2e^2 = 0, so C1 = -C2e^2
for x = 0: C1 + C2e^2 = 0
substituting gives: -C2e^2 + C2e^2 = 0

Does this suffice? Is there a way to get C1 = 0 and C2 = 0 explicitly?

Answer 1

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