What is the rank in matrices

The matrix rank is determined by the number of independent rows or columns present in it. A row or a column is considered independent, if it satisfies the below conditions.
1. A row/column should have atleast one non-zero element for it to be ranked.
2. A row/column should not be identical to another row/column.
3. A row/column should not be proportional (multiples) of another row/column.
4. A row/column should not be should not be a linear combination of another row/column.

A row or a column is ranked only if it meets the above conditions. For example, the rank of the below matrix would be 1 as the second row is proportional to the first and the third row does not have a non-zero element.
 

[1 2 3][2 4 6]       [0 0 0]