- #1
bjgawp
- 84
- 0
I'm considering the problem: Given [tex]c \in \bold{F}[/tex], [tex]v \in V[/tex] where F is a field and V a vector space, show that [tex]cv = 0, v \neq 0 \ \Rightarrow \ c = 0 [/tex]
I've been wrapping my head around this one for a while now but I can't seem to get it. Proving that if cv = 0 and v [tex]\neq[/tex] 0 implies v = 0 is easy since we can simply multiply by [tex]c^{-1}[/tex] but in vector space, we don't have that kind of inverse for vectors seeing how we only have scalar multiplication.
I've been wrapping my head around this one for a while now but I can't seem to get it. Proving that if cv = 0 and v [tex]\neq[/tex] 0 implies v = 0 is easy since we can simply multiply by [tex]c^{-1}[/tex] but in vector space, we don't have that kind of inverse for vectors seeing how we only have scalar multiplication.