Let f1(t)=e^t, f2(t)=te^t, f3(t)=t^2e^t, and let V=Span(f1,f2,f3) in the infinite continuous functions. Let T:V-->V be give by T(f)=f''-2f'+f. Decide whether T is diagonalizable.(adsbygoogle = window.adsbygoogle || []).push({});

We learned a theorem that this will be diagonalizable if and only if the geometric multiplicity of each eigenvalue equals its algebraic multiplicity.

What I am having trouble with is translating this into a way to find geometric and algebraic multiplicity. I'm not entirely sure what to do when I'm not given a matrix, since that's how we did it in class.

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# Homework Help: Let f1(t)=e^t, f2(t)=te^t, f3(t)=t^2e^t, and let V=Span(f1,f2,f3) in

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