Rank

The rank of a matrix is the number of Pivots in it's Row-Echelon-Form (REF), or equivalently, it is the number of non-zero rows in it's REF.

Example:

Given where , , there are three cases:

  1. If , then the system is inconsistent no solution.
  2. If unique solution.
  3. if infinite solutions.

for all matrices

Example:

Go to Gaussian Elimination With A Parameter to see a worked example of how to turn a system of equations with a parameter into each of the cases listed above.