Originally Posted by

**scorpion007** I keep getting inconsistent results with this one. I can't find a single vector that belongs to both sets. Is the question correctly formed?

**Question:**

Two subspaces S and T of R^3 are spanned by {(1,1,-2), (-1,1,0) } and { (1,1,0), (0,-11,1)} respectively. Find a non-zero vector X that belongs to $\displaystyle S\cap T$.

This is what I did:

We need $\displaystyle X=a(1,1,-2)+b(-1,1,0) = c(1,1,0) + d(0,-11,1)$.

So,

$\displaystyle a-b=c$

$\displaystyle a+b=c-11d$

$\displaystyle -2a=d$

Right so far?

From here I can't get any consistent solution for a, b such that $\displaystyle a(1,1,-2)+b(-1,1,0) = c(1,1,0) + d(0,-11,1)$.