Let V be a real vector space with basis v₁, v2. Define , where A = (043) = [₁ 2] ₁ Assuming that this makes V,. into an inner product space, find an orthonormal basis w₁, W₂ with respect to this inner product in terms of V₁, V2. Vi • Vj = Ajj,' Select one: ○ w₁ = v₁/√√5, W2 = (v₁ – 5v₂)/√/45 W₁ = (v₁ + 2v₂)/√√5, W₂ = (v₁ − v₂)/√√/2 None of the others apply The associated quadratic form q(v) = v - v for the stated dot product is not in fact positive definite, hence there is no orthonormal basis in this case. w₁ = (√5v₁ + √2v2)/√√7, w2 = (-v1 - v₂)/√√/2

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