Why is the following tuple of vectors not a basis of $\mathbb{R}^{2}$? $\left ( \left ( \begin{array}{c} 1\\ 0\\0 \end{array} \right ), \left ( \begin{array}{c} 0\\ 1\\0 \end{array} \right ) \right )$
I would've thought that just like $\left ( \left ( \begin{array}{c} 1\\ 0\end{array} \right ), \left ( \begin{array}{c} 0\\ 1 \end{array} \right ) \right )$ the 1st tuple would span $\mathbb{R}^{2}$ and the vectors clearly linearly independent...
Hopefully I'm not fundamentally misunderstanding something, I'm doing one of those "self-test at the end of the chapter only solutions, no explanations" things. It'd be great if anyone could offer a brief explanation so that I can move on... thanks!