[noot_chy]

Definition
The rank ofamatrix A,denoted r(A),is the number
of non-zero rows in the row-reduced echelon formof A.Thus, r(A) is equal
to the number of leading1’s in the row-reduced echelon form of the matrix A.

Definition
We say that an m*n matrix A has fullrank if r(A)= n,
i.e.,if the RREFof A has a leading one in each column.