A matrix A is said to be of rank r if there is at least one non zero minor of order r and every minor of order r+1 is zero.

 

Eg:

 

Consider a matrix A,

[2   -1   5]  

|3    0   6|

[4    1   7]

 

|A|=0

 

So the minor of third order is zero

 

There exists a minor of second order

|3    0|

|1    4|

 

which is equal to 3

 

Thus a minor of second order is not zero.

 

So rank of A is 2