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## Homework Statement

Show that in n-dimensional space, any n+1 vectors are linearly dependent.

Ok... I actually know this is true, but I'm lost as to how to show it.

## Homework Equations

Vectors are linearly independent if the only solution to [tex]\alpha_{1}|v_{1}>+\alpha_{2}|v_{2}>+...+\alpha_{n}|v_{n}>+\alpha_{n+1}|v_{n+1}>=|0>[/tex] is the trivial solution (where [tex]\alpha_{1}=...=\alpha_{n}=\alpha_{n+1}=0[/tex]).

## The Attempt at a Solution

So far I'm only making a statement that each vector has n elements but there are n+1 unknowns, so if the vectors are in the vector space, then they must be linearly dependent.

Any suggestions to improve my answer would be greatly appreciated.