Q:

Removal of a vector from a basis => Resulting set doesn't span the vector space.

Suppose ${v_{1},v_{2},\ldots,v_{n}}$ is a basis for a vector space $V$.
Show that if any $v_{j}$ is removed from the basis, the resulting set of $n-1$ vectors does not span $V$. It seems obvious. But I do not know how to prove?

A:

If you choose the definition of basis:  

A linearly independent spanning set for a vector space $V$ is called a basis for $V$

so if you remove the vector $v_j$ can you express this vector by a linear combination of the other vector of the basis? if your answer yes then the vectors of the basis aren't linearly independant and if your answer no then the vectors don't span the space.

