Question

how to find a rank of a matrix?

Answer 1

there are many methods....
one fast method is to use Gauss Echelon Form or Row equivalent canonical form of a matrix...
ie.convert the first element of the first row into 1(or any non 0 element)...make all the elements under this 1 into 0....now change the second element of second row into 1 and all elements under it to 0.similarly 3rd element of third row to 1 and all under it to 0....then the rank of the matrix is the no. of non 0 rows