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Math Help - Linear Transformation

  1. #1
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    Linear Transformation

    Here is the problem:



    How do I do this? Help please!!
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  2. #2
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    Quote Originally Posted by Phyxius117 View Post
    Here is the problem:



    How do I do this? Help please!!

    Calculate the matrix of T wrt ANY basis of P_2 and then calculate its determinant...

    Tonio
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  3. #3
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    For example, a good basis for P2 (the space of polynomials of degree at most 2) is e_1= 1, e_2= x, e_3= x^2. Apply the transformation to each of those and write the result as a linear combination of them. The numbers multiplying each vector in the linear combination will be one column of the matrix.

    (When I first looked at this, I made a very foolish error. I assumed that, like the derivative operator itself, this would have non-trivial kernel and so would be non-invertible and have determinant 0. Fortunately, however, I chose to check that and discovered it was not true!)
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