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[All Steps] Let u=(u_1,u_2) and v=(v_1,v_2) be vectors is R^2, and define the function T(u,v)=u_1v_1+3u_1v_2+3u_2v_1+10u_2v_2 Does the function define a

Question: Let \(u=\left( {{u}_{1}},{{u}_{2}} \right)\) and \(v=\left( {{v}_{1}},{{v}_{2}} \right)\) be vectors is \({{\mathbb{R}}^{2}}\), and define the function

\[T\left( u,v \right)={{u}_{1}}{{v}_{1}}+3{{u}_{1}}{{v}_{2}}+3{{u}_{2}}{{v}_{1}}+10{{u}_{2}}{{v}_{2}}\]

Does the function define a inner product on \({{\mathbb{R}}^{2}}\) ?

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