.So my professor told us this and I am trying to see how its true.
You have a vector space V. v1 and v2 are elements of V. V is over an arbitrary field F-sub-q (q not equal to two), so if it was F-sub-3 for example, its elements would go 0,1,2,0,1,2...
Uuh? No, the elements of are only
so say you multiply 2 * 2 which would normally equal 4, here would equal 0.
No, again: in , since
v1 and v2 are non-collinear, so v1 does not equal lambda * v2 for for any lambda in F-sub-q.
He made the claim that v1+v2 is linearly independent of v1-v2.
In any vector space, two vectors are lin. ind. iff none of them is a scalar multiple of the other one, so assume . As are lin. ind. the above is possible iff ...and this cannot be UNLESS the field's characteristic is 2...
I thought about the definition of that, so if x(v1+v2)+y(v1-v2)=0vector, then x,y MUST be 0. I am just having a hard time proving that.
Any and all help would be much appreciated!!