Let <>: P₂ x P₂ → R be defined by = aobo + a₂b₁ + a₂b2. Prove that <,> is an inner pro

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Let P X P R Be Defined By Ao A X A X 2 Bo B X B X Aobo A B A B2 Prove That Is An Inner Pro 1 (204.81 KiB) Viewed 18 times

Let <>: P₂ x P₂ → R be defined by <ao+a₁x + a₂x²2, bo + b₁x + b₂x² >= aobo + a₂b₁ + a₂b2. Prove that <,> is an inner product on P₂ (R). (i) (ii) Find the angle between the vectors f(x) = 1- x and g(x) = x². ✓ (1) Show that the vectors W₁ = (0,2,0), W₂ = (3,0,3), w3 = (-4,0,4) form an orthogonal basis for R3 with Euclidean inner product and use that basis to an orthonormal basis by normalizing each vector. V (1) Express the vector u = (1,2,4) as a linear combination of the orthonormal basis vector obtained in part (i). V