Which of the following defines a valid inner product on R2\mathbb{R}^2R2?
⟨u,v⟩=u1v1−u2v2\langle u, v \rangle = u_1 v_1 - u_2 v_2⟨u,v⟩=u1v1−u2v2
⟨u,v⟩=u1v1+2u2v2\langle u, v \rangle = u_1 v_1 + 2u_2 v_2⟨u,v⟩=u1v1+2u2v2
⟨u,v⟩=u1v2+u2v1\langle u, v \rangle = u_1 v_2 + u_2 v_1⟨u,v⟩=u1v2+u2v1
⟨u,v⟩=u12v12+u22v22\langle u, v \rangle = u_1^2 v_1^2 + u_2^2 v_2^2⟨u,v⟩=u12v12+u22v22