Kernel and Linear transformation

[Hockeystar]

Homework Statement

U = [Polynomial of degree 3 such that 3p(1) = p(0)]

Find the basis of U and find a linear transformation T: P₃ ---> R such that U is the kernel of T.

Homework Equations

The Attempt at a Solution

The basis part is easy.
3p(1) = p(0)
3a + 3b + 3c +d = d
c= -b-a

Basis : {<1,0,-1,0>,<0,1,-1,0>,<0,0,0,1>}

The kernel part makes no sense (prof never went over this in class). I know kernel means T(v) = 0 Could the transformation just be R = {a-a, b-b, -(b+a) +(b+a), d-d}

 

[Outlined]

solve:

<1,0,-1,0> * x₁ + <0,1,-1,0> * x₂ + <0,0,0,1> * x₃ = 0