(a) Prove that the only subspaces of $ \Bbb{R}$ are $ \Bbb{R}$ and the zero subspace. (b) Prove that a subspace of $ \Bbb{R}^2$ is $ \Bbb{R}^2$ , or the zero subspace, or consist of all scalar multiples of some fixed vector in $ \Bbb{R}^2$ . My attempt: (a) Assume towards contradiction, $ \exists A$Read more