- #1
stunner5000pt
- 1,461
- 2
Suppose that {v1,v2,...,vn} is a minimal spanning set for a vector space V. That is V = span {v1,v2,...,vn} and V cannot be spanned by fewer than n vectors. Show that {v1,v2,...,vn} is a basis of V
to be a basis for V then V = span (v1,v2,...,vn}
we already have that
suppose one of thise vectors was not linearly dependant then the number of vectors in the span is less than n. But V = span of n vectors
so the set of vectors must be lienarly independant
to be a basis for V then V = span (v1,v2,...,vn}
we already have that
suppose one of thise vectors was not linearly dependant then the number of vectors in the span is less than n. But V = span of n vectors
so the set of vectors must be lienarly independant