Let V be a real vector space with basis v₁, V₂ and define a dot product by V₁ V₁ = 1, V₁ V₂ = V₂ V₁ = A, V₂ V₂ = 2, where A E R is fixed. For what values of A does (V,.) become an inner product space with the stated dot products? (Hint: you may wish to diagonalise the associated quadratic form q(x, y) = x² + 2xxy + 2y².)

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