Exercise 4

For which $n$ is the space isomorphic to $\mathbb{R}^{n}$?

• $\mathcal{P}_{4}$

• $\mathcal{P}_{1}$

• $\mathcal{M}_{2\!\times\!3}$

• the plane $2x-y+z=0$ subset of $\mathbb{R}^{3}$

• the vector space of linear combinations of three letters $\{\hskip 1.00006ptax+by+cz\mid a,b,c\in\mathbb{R}\hskip 1.00006pt\}$