# Problem set 2 2.2.1. section 2.1. (1) let l be the operator defined by l() = (á - a) a. show that l is linear. b. show

###### Question:

Problem set 2 2.2.1. section 2.1. (1) let l be the operator defined by l() = (á - a) a. show that l is linear. b. show that the kernel of l is a vector space. c. let g(t) be a non-trivial function. show that the collection of vector-valued functions which satisfy = g(t) do not form a vector space. d. show that the difference between any two functions, t1, t2 which satisfy l(t) = g(t) is in the kernel of l. ) read the statement of abel's theorem. a. what are the hypotheses of abel's theorem as stated in the notes? b. what are the conclusions of abel's theorem as stated in the notes? c. show that ? i(t) = (+) and tz(t) = (2) are solutions to = ( ) [e). d. what are the largest intervals on which õi(t) and 72(t) are linearly indepen- dent? e. does this violate abel's theorem as stated in the notes? why or why not?

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