Exercise 1

Name the zero vector for each of these vector spaces.

• The space of degree three polynomials under the natural operations.

• The space of $2\!\times\!4$ matrices.

• The space $\{\hskip 1.00006pt\text{$f\colon[0..1]\to\mathbb{R}$}\mid f\text{ is continuous}\hskip 1.00006pt\}$.

• The space of real-valued functions of one natural number variable.