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    Define h_1,h_2,H_3 \in \mathbb{R} by  h_1(x)=x^2+3x-2, h_2(x)=x^2-x+1 and h_3(x)=x^2-5x-1. Define C:=[h_1,h_2,h_3]. Assuming C is an order basis for P_2(\mathbb{R}). Construst the change of co-ordinates matrix, A, that converts C-co-ordinates to B-co-ordinates. Compute the inverse of A.

    Please help! I just need to understand how to do this kind of question for my Linear Algebra exam but I have absolutely no clue.

    Specify what it is that you don't know:

    1) Do you know what P_2(\mathbb{R}) is? (...and did you mean to say h_1,h_2,h_3 \in P_2(\mathbb{R}) or are you just confused?)
    2) Do you know what an (ordered) basis is?
    3) Do you know what a change of basis matrix is and what it does?
    4) Do you know what the ordered basis B is? (I am assuming it is the standard basis for P_2(\mathbb{R}) unless you were given something otherwise)
    5) Do you know what the inverse of a matrix is?
    6) Do you know what the inverse of a change of basis matrix is?
    7) Do you know how to invert a matrix in general?
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Updated: May 16, 2013
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