Define T P5 rightarrow P5 by Tp p What is the kernel of T U

Define T: P5 rightarrow P_5 by T(p) = p\'. What is the kernel of T? (Use a_0, a_1, a_2, ... as arbitrary constant coefficients of 1, x, x^2, ... respectively.) ker(T) = {p(x) =: a_i R}

Solution

since T mapping from p₆ to p₅

ker(T) = { p(x) = a₀ + a₁x +a₂x² + a₃x³ + a₄x⁴ }