ECHEL ON FORM OF A MATRIX
A matrix A is said to be in Echelon form if either A is the null matrix or A satisfies the following conditions :
(i) Every non-zero row in A proceeds every zero row.
(ii) The number of zeros before the first non-zero element in a row is less than the number of such zeros in the next row.
It can be easily proved that the rank of a matrix in Echelon form is equal to the number of non-zero rows of the matrix.
The rank of the matrix
is 2 because it is Echelon form and it has two non
zero rows. The matrix
is not in Echelon form, because the number of zeros in second row is not less than the number of zeros in the third row.
