**Rank of a Matrix**

The rank of a matrix is the number of linearly independent row or columns in the matrix.

To calculate the rank:

- Reduce the matrix to to row-echelon form
- Count the number of non-zero rows in the row-echelon matrix

OR

If the matrix is a square matrix (i.e. *n x n*) then the rank is n if and only if the determinant of the matrix is not equal to zero.