4. (18 pts) Recall P4 is the set of polynomials with degree 4. Let V = {f(x) = P₁ | f(2)= 0 and f(1) = f(-1)}, i.e., it

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4 18 Pts Recall P4 Is The Set Of Polynomials With Degree 4 Let V F X P F 2 0 And F 1 F 1 I E It 1 (31.61 KiB) Viewed 28 times

4. (18 pts) Recall P4 is the set of polynomials with degree 4. Let V = {f(x) = P₁ | f(2)= 0 and f(1) = f(-1)}, i.e., it is the set of polynomials with degree ≤ 4 such that f(2)= 0 and f(1) = f(-1). (a) Show that V is a subspace of P4. (b) Show that f(x) = ao + a₁ + a₂x² + a3x³ + a42¹ € V if and only if ao EN(1 EJ [1 2 4 8 16] 2020 16]). a3 0.4 (c) Find a basis for V and hence find the dimension. a1 a2