Kernel of linear transformation

[AndreTheGiant]

Homework Statement

I am having lots of trouble understanding how to get the kernel of linear transformations. I get that you basically set it equal to zero and solve.

T: P3 → P2 given by T(p(x)) = p΄΄(x) + p΄(x) + p(0)

Find ker(T)

The Attempt at a Solution

So P3 = ax^3 + bx^2 + cx +d
then the linear transformation should be

6ax + 2b + 3ax2 + 2bx + c + d


but how do i find ker T?

 

[Dick]

You've got the transformation right. You want the result to be a zero polynomial. A polynomial is only zero if the coefficient of each power of x is zero.