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## Homework Statement

If I e.g. want to find the kernel and range of the linear opertor on P_3:

L(p(x)) = x*p'(x),

then we can write this as L(p'(x)) = x*(2ax+b). What, and why, is the kernel and range of this operator?

## The Attempt at a Solution

The kernel must be the x's where L(p'(x)) = 0, so do I just solve the equation?

The range is the elements that span the polynomial, so it is span{(x^2,x)}?

Hope you can help.