7. Assume that Vi, i = 1,2 are vector spaces over F E {R, C} and (,), i = 1, 2 is an inner product on V₂. Set V = V₁ V₂ and define (, ): V x V → F by ((U₁, U2), (v₁, v₂)) = (U₁, v₁)₁ + (u2; v₂) 2 for u₁, v₁ € V₁, U2, v2 € V₂. Determine whether (, ) is an inner product on V. Prove your conclusion.

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