Matrix Representation of Differentiation Operator for Subspace S in C[a,b]

[electricalcoolness]

Another problem I can't figure out how to start.

Let S be the subspace of C[a,b] spanned by e^x , xe^x , (x^2)e^x . Let D be the differentiation operator of S. Find the matrix representing D with respect to [e^x, xe^x, (x^2)e^x ]

 

[Hurkyl]

Well, what have you tried? Do you know how to find a matrix representing a linear transformation?

 

[Diophantus]

Hint

Hint: Try using the differntial operator on each of your bases and then see if you can rewrite each of the results as a linear combination of the bases. After that you may wish to consider the relevance of the coordinate vectors of your results.