# When are vectors linearly independent?

A (finite) set of vectors $v_1, v_2...v_m$is said to be linearly independent if and only if the equality $k_1v_1+k_2v_2+...k_mv_m=0$ is true exactly when all the k values are 0.

This is equivalent to saying you can't come up with any linear combination of $v_1$ and $v_2$ that equals $v_3$, or $v_1...v_3$ that equals $v_4$... or $v_1...v_{m-1}$ that equals $v_m$.

If a set of vectors are not linearly independent, then they are linearly dependent.

## Alumni Liaison

Basic linear algebra uncovers and clarifies very important geometry and algebra.

Dr. Paul Garrett