Exercise 5

For each, list three elements and then show it is a vector space.

• The set of three-component row vectors with their usual operations.

• The set

  $\{\hskip 1.00006pt\begin{pmatrix}x\\ y\\ z\\ w\end{pmatrix}\in\mathbb{R}^{4}\mid x+y-z+w=0\hskip 1.00006pt\}$

  under the operations inherited from $\mathbb{R}^{4}$.