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(adsbygoogle = window.adsbygoogle || []).push({});

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

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# Homework Help: Linear independance

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