Here is the problem:

http://i10.photobucket.com/albums/a1.../Problem16.jpg

How do I do this? Help please!!

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- Oct 5th 2010, 04:09 PMPhyxius117Linear Transformation
Here is the problem:

http://i10.photobucket.com/albums/a1.../Problem16.jpg

How do I do this? Help please!! - Oct 5th 2010, 08:01 PMtonio
- Oct 6th 2010, 04:21 AMHallsofIvy
For example, a good basis for P2 (the space of polynomials of degree at most 2) is $\displaystyle e_1= 1$, $\displaystyle e_2= x$, $\displaystyle e_3= x^2$. 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!)