Let Consider the complex inner product space C³ with the usual inner product (u, v) = ₁V₁ + U₂ V₂ + UzV3. and let W = span {V₁, V₂}. (a) Compute the following inner products: (V₁, V₁) = (V₁, V₂) = = (V₂, V₁) = (V2, V₂) = V₁ = and V₂ = -3i 2i

T: P2 P2 defined by T(a + bx + cx²) = a + b(x + 8) + b(x + 8)² Find the following images of the function for vectors p₁(x) = a₁ + b₁x + c₁x² and p₂(x) = a₂ + b₂x + c₂x2 in P₂ and the scalar k. (Give all answers in terms of a₁, b₁, C₁, 22, b₂, C₂ and c.) T(P₁) + T(P₂): = T(P1 + P₂) = cT (P1) = T(CP1) = Determine whether T is a linear transformation. 4 Olinear transformation O not a linear transformation

Since it's an if and only if proof, don't you have to prove "if linearly dependent, then scalar multiples" and then "if scalar multiple, then linearly dependent"?

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