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 \({{\mathbb{R}}^{2}}\) ?