Exercise 2

Find the additive inverse, in the vector space, of the vector.

• In $\mathcal{P}_{3}$, the vector $-3-2x+x^{2}$.

• In the space $2\!\times\!2$,

  $$\begin{pmatrix}1&-1\\ 0&3\end{pmatrix}.$$

• In $\{\hskip 1.00006ptae^{x}+be^{-x}\mid a,b\in\mathbb{R}\hskip 1.00006pt\}$, the space of functions of the real variable $x$ under the natural operations, the vector $3e^{x}-2e^{-x}$.