First, let's find the weighted Euclidean inner product <uv> using the given formula:
<uv> = 3uv + 2u^2v^2
Substituting the values of u and v:
<uv> = 3(1)(2,1) + 2(1,-1)^2(2,1)^2
Simplifying:
<uv> = 3(2,1) + 2(1,-1)^2(2,1)^2
<uv> = 3(2,1) + 2(1,-1)^2(4,1)
<uv> =
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