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Vectors & Spaceshard
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Let V=P2V = P_2V=P2​. Consider the linear functional ϕ(p)=p(1)+p′(0)\phi(p) = p(1) + p'(0)ϕ(p)=p(1)+p′(0). Find the polynomial q∈P2q \in P_2q∈P2​ such that ϕ(p)=⟨p,q⟩\phi(p) = \langle p, q \rangleϕ(p)=⟨p,q⟩ using the inner product ⟨p,q⟩=a0b0+a1b1+a2b2\langle p, q \rangle = a_0 b_0 + a_1 b_1 + a_2 b_2⟨p,q⟩=a0​b0​+a1​b1​+a2​b2​.