Exercise 3

Represent the vector with respect to the basis.

• $\begin{pmatrix}1\\ 2\end{pmatrix}$, $B=\langle\begin{pmatrix}1\\ 1\end{pmatrix},\begin{pmatrix}-1\\ 1\end{pmatrix}\rangle\subseteq\mathbb{R}^{2}$

• $x^{2}+x^{3}$, $D=\langle 1,1+x,1+x+x^{2},1+x+x^{2}+x^{3}\rangle\subseteq\mathcal{P}_{3}$

• $\begin{pmatrix}0\\ -1\\ 0\\ 1\end{pmatrix}$, ${\cal E}_{4}\subseteq\mathbb{R}^{4}$