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I'm a new student and don't have any basics for linear algebra. thanks

1. The problem statement, all variables and given/known data

Q1. Let X be the vector space of polynomials of order less than or equal to M.

a) show that the set B = {1,x,...x^M}

b) consider the mapping T from X to X as defined as :

f(x)=T g(x) = d/dx g(x)

(i) Show that T is linear

(ii) Derive matrix representation for T in terms of the basis B

(iii) What are the eigenvalues of T

(iv) Compute one eigenvector associated with one of the eigenvalues

Thanks again

2. Relevant equations

3. The attempt at a solution

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# Homework Help: Polynomial Mapping

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