Exercise 3.F.27

Proof. We have

p ∈P5(ℝ) : ψ(p) = 0 for every ψ ∈ null ⁡ T′

=

p ∈P5(ℝ) : ψ(p) = 0 for every ψ ∈ span ⁡ (φ)

=

p ∈P5(ℝ) : φ(p) = 0

=

p ∈P5(ℝ) : p(8) = 0

Where the first equation follows from Exercise 25 and the second from 3.107. □