Prove: If V is a finite dimensional vector space and T is in L(V), then there exists a finite list of scalars ao,a1,a2,.....,an, not all 0 such that(adsbygoogle = window.adsbygoogle || []).push({});

aoX + a1T x + a2T^2 x..... + anT^n x = theata

for all x in V

my hint for the question is:

the powers of T are defined as T^0 = I, T^1 = 1, T^2 = TT, T^3 = T^2T

consider the sequence I, T, T^2, T3,..... in the finite-dimensional vector space L(V).

please help, have have no clue what to do. Any help would be greatly appriciated.

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# Homework Help: Algebra proof!

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