(Solved): (a) Describe geometrically as best as you can the subspaces of \( \mathbb{R}^{3} \) spanned by the ...

(a) Describe geometrically as best as you can the subspaces of \( \mathbb{R}^{3} \) spanned by the following sets of vectors. \[ \begin{array}{l} \left\{\left[\begin{array}{l} 1 \\ 0 \\ 0 \end{array}\right]\right\} \\ \left\{\left[\begin{array}{l} 1 \\ 0 \\ 0 \end{array}\right] \rightarrow\left[\begin{array}{l} 0 \\ 1 \\ 0 \end{array}\right]\right\} \end{array} \] b) Express the following set of vectors as the span of some vectors to show that this set is a subspace. Can you give a geometric description of the set? \[ W=\left\{\left[\begin{array}{c} 2 x+y-z \\ y \\ z \\ -x+3 z \end{array}\right] ; x, y,=\text { real numbers }\right\} \]