The Rank of the following matrix is
⎡⎢ ⎢ ⎢⎣1003011200000011⎤⎥ ⎥ ⎥⎦−−−−−−−−−−−
Lets convert it into Echelon form
For that all no zero rows should be below all zero rows.
Interchange, R3 & R4
⎡⎢ ⎢ ⎢⎣1003011200110000⎤⎥ ⎥ ⎥⎦
This is now in Echelon form and the number of non zero rows are 3. Therefore Rank is 3.