$\displaystyle U=[(1,1,1), (1,0,-1)]$

$\displaystyle V=[(2,1,1), (1,0,1)]$

Find a basis for the set $\displaystyle U\cap V$

SOLVED

-----------------------------------------

While we're at it, how do I mathematically prove that $\displaystyle dim(M)=3$ if $\displaystyle M=\{(x_1, x_2, x_3, x_4)\in R^4: x_1+x_2+x_3=0\}$

EDIT: Another one:

$\displaystyle U_1 \subseteq V$, $\displaystyle U_2 \subseteq V$ and $\displaystyle U_1\oplus U_2 = \{\}$

Prove that $\displaystyle dim(U_1) + dim(U_2) \leq dim(V)$