# Linear Transformation

• October 5th 2010, 04:09 PM
Phyxius117
Linear Transformation
Here is the problem:

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

How do I do this? Help please!!
• October 5th 2010, 08:01 PM
tonio
Quote:

Originally Posted by Phyxius117
Here is the problem:

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

How do I do this? Help please!!

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

Tonio
• October 6th 2010, 04:21 AM
HallsofIvy
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!)