Let V be a vector space over field F.Let g,f1,f2,...fk belong to V* i.e;dual of v,then show that g belongs to span{f1,f2,...,fk} if and only if intersection of kernel(fi) i=1 to k is subset of Kernel(g)..
Let V be a vector space over field F.Let g,f1,f2,...fk belong to V* i.e;dual of v,then show that g belongs to span{f1,f2,...,fk} if and only if intersection of kernel(fi) i=1 to k is subset of Kernel(g)..
Thank you in advance..
In any vector space we have that . We can assume are lin. indep.
Thus in our case:
OTOH, if then is lin. indep, so we can complete it to a basis of , and let be the dual basis of and we're done.