In this learning object, we're going to look at vectors which are "linearly dependent" or "linearly independent". The word "dependent" means that some vectors can be expressed in terms of others - they depend on the others. The word "linear" describes the form of that dependence - as a linear combination. On the following pages, we'll look at
  1. The formal definition of linear dependence and linear independence,
  2. Some examples of linearly independent and linearly dependent vectors,
  3. An equivalent, more practical definition of linear independence.
Prerequisites: A basic knowledge of vectors and vector calculations and an understanding of what the span of a set of vectors is. (See the learning object Linear Spans for more information.) Also, a little about linear systems and their solutions (for examples) and what trivial and non-trivial solutions are.
Keywords: linearly independent vectors, linearly dependent vectors, linear dependence relation among vectors, trivial and non-trivial solutions