Suppose and .
let be a base for and a basis for . Set .
You can easily show, I hope, that and
Hi guys.
i need help to prove the following:
"Let be subspace of , such that there exist one and only one subspace for wich .
Prove that must be a trivial subspace."
this is what i've tried so far:
let's suppose there exist only one subspace .
and let's suppose it is not trivial.
let be the base for .
let be the base for .
let ,
since , there exist one and only one linear combination such that:
according to the assumption, there exist only one , but there are infinite number of bases for .
therefor, i can define new base for W and use other scalares...
now, i'm not sure if i'm in the right way or where, if at all, lies the contradiction.
i could really use some direction here.
thanks in advanced!