Exercise 8

Find a basis for each.

• The subspace $\{\hskip 1.00006pta_{2}x^{2}+a_{1}x+a_{0}\mid a_{2}-2a_{1}=a_{0}\hskip 1.00006pt\}$ of $\mathcal{P}_{2}$

• The space of three-wide row vectors whose first and second components add to zero

• This subspace of the $2\!\times\!2$ matrices

  $\{\hskip 1.00006pt\begin{pmatrix}a&b\\ 0&c\end{pmatrix}\mid c-2b=0\hskip 1.00006pt\}$