Using the definition in Problem 35, prove that if r1, r2 and,r3 , and are distinct real...

Using the definition in Problem 35, prove that if r₁, r₂ and,r₃ , and are distinct real numbers, then the functions e^r1t ,e^r2t and e^r3t are linearly independent on . [Hint: Assume to the contrary that, say, for all t. Divide by e^r2t to get and then differentiate to deduce that are linearly dependent, which is a contradiction. (Why?)]