Exercise 22

Let $h\colon\mathbb{R}^{n}\to\mathbb{R}^{m}$ be a homomorphism.

• Show that the image under $h$ of a line in $\mathbb{R}^{n}$ is a (possibly degenerate) line in $\mathbb{R}^{m}$.

• What happens to a $k$-dimensional linear surface?