- #1
Treadstone 71
- 275
- 0
If a,b,c are vectors in an R-vector space then their sums a+b, a+c, b+c are also linearly independent. If R is replaced by Z_2 then this fails, because there's the nontrivial solution to
x(a+b)+y(a+c)+z(b+c)=0
where x=y=z=0 or x=y=z=1
right?
x(a+b)+y(a+c)+z(b+c)=0
where x=y=z=0 or x=y=z=1
right?