Let V = R be equipped with the operations x1 X2 ko x1 x2. Y Y2...

Transcribed Image Text:

Let V = R² be equipped with the operations x1 X2 ko x1 x2. Yı Y2 = = - 3 x₁ + Yı x2 + y2 + 1 kx₁ - 3k +3] kx₂ + k-1 Prove, by definition (showing all axioms hold in general) that V is a vector space. Note: As always, keep your proof general and don't select specific vectors or scalars. Note: You are not given the fact or assumption that V is a vector space (this is what you're trying to prove). Thus, you are not allowed to use theorems that use the assumption that V is a vector space. Let V = R² be equipped with the operations x1 X2 ko x1 x2. Yı Y2 = = - 3 x₁ + Yı x2 + y2 + 1 kx₁ - 3k +3] kx₂ + k-1 Prove, by definition (showing all axioms hold in general) that V is a vector space. Note: As always, keep your proof general and don't select specific vectors or scalars. Note: You are not given the fact or assumption that V is a vector space (this is what you're trying to prove). Thus, you are not allowed to use theorems that use the assumption that V is a vector space.