You are given a set S in a vector space V. Determine whether S spans V. Justify your
answers.
(i) V = R³ and
S = { (1,2,-1), (0, 1, 1), (2, 1, -5), (-3, 1, 10) }
(ii) V = M<sub>2x2</sub>(R) and
S = { $$\begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix}$$, $$\begin{pmatrix} 1 & 0 \\ 0 & -1 \end{pmatrix}$$, $$\begin{pmatrix} 1 & 1 \\ 0 & 0 \end{pmatrix}$$, $$\begin{pmatrix} 1 & 1 \\ 1 & 0 \end{pmatrix}$$ }