Let S be a subset of an ndimensional vector space V and supp

Let S be a subset of an n-dimensional vector space V, and suppose S contains fewer than n vectors. Explain why S cannot span V.

Solution

suppose V is an n-dimensional vector space.

Given \'S\' is a subset of V that contains fewer than n vectors.

If \'S\' spans V then the dimension of V becomes less than \'n\' which is not true.

Therefore S cannot span V.