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**mtmath** show that every set with more than n vectors is necessarily linearly dependent in a n-dimensional vector space.

The following shows how i give it a try. am i getting things right. is there any way of tackling the same problem?

proof:

suppose B = {e1,e2,...,en} is a basis for **V**. i.e dim(**V**)= n.

Let S = {s1,s2,...sN} n < N.

then 1 of the elements in S can be expressed as a linear combination of other elements. say s1.

s1

= k1*s2 + k2*s2 + ...+kN*sN

= k1(a1*e1 +... + an*en) + k2(b1*e1 +...+ bn*en) +...+ KN(x1*e1 +...+xN*en)

= ...(some steps)

= y1*e1 + y2*e2 + ... + yn*en