Does $\{u_1, u_2, u_3, u_4\}$ spanning $\mathbb R^3$ mean that $\{u_1,u_2,u_3\}$ also does? Since it's a subset? Does $\{u_1, u_2, u_3, u_4\}$ spanning $\mathbb R^3$ mean that $\{u_1,u_2,u_3\}$ also does?  Since it's a subset? A little unclear about this...

A concrete example:
$$u_1=(1,0,0),u_2=(2,0,0),u_3=(0,1,0),u_4=(0,0,1)$$
$\{u_1,u_2,u_3,u_4\}$ clearlly spans $\mathbb{R}^3$.
On the other hand $u_4 \notin span\{u_1,u_2,u_3\}$, and therefore $\{u_1,u_2,u_3\}$ does not span $\mathbb{R}^3$.
