What is 'Linear Independence'?

Approach: Define vectors that cannot be expressed as a combination of others.

A set of vectors is linearly independent if no vector in the set can be written as a linear combination of the others. Mathematically, c1v1 + ... + cnvn = 0 implies all ci = 0.

Follow-up: What is the rank of a matrix with 3 linearly independent columns?

Key concepts: basis, spanning set, rank.