##### Activity3.5.2

We will look at some more subspaces of $$\real^2\text{.}$$

1. Explain why a line that does not pass through the origin, as seen to the right, is not a subspace of $$\real^2\text{.}$$

2. Explain why any subspace of $$\real^2$$ must contain the zero vector $$\zerovec\text{.}$$

3. Explain why the subset $$S$$ of $$\real^2$$ that consists of only the zero vector $$\zerovec$$ is a subspace of $$\real^2\text{.}$$

4. Explain why the subspace $$S=\real^2$$ is itself a subspace of $$\real^2\text{.}$$

5. If $$\vvec$$ and $$\wvec$$ are two vectors in a subspace $$S\text{,}$$ explain why $$\span{\vvec,\wvec}$$ is contained in the subspace $$S$$ as well.

6. Suppose that $$S$$ is a subspace of $$\real^2$$ containing two vectors $$\vvec$$ and $$\wvec$$ that are not scalar multiples of one another. What is the subspace $$S$$ in this case?

in-context