Linear dependence and relations
Suppose
View code
Suppose $V$ is a vector space, and ${\bf v}_1, {\bf v}_2, \ldots, {\bf v}_n$ are in $V$. Prove that either ${\bf v}_1, \ldots, {\bf v}_n$ are linearly independent, or there exists a number $k\leq n$ such that ${\bf v}_k$ is a linear combination of ${\bf v}_1,\ldots, {\bf v}_{k-1}$.