consider these row values as R1=[1 1 1], R2=[1 -1 0], R3=[1 1 1] assume R2-->R2-R1, you will get R2=[0 -2 -1] assume R3-->R3-R1, you will get R3=[0 0 0] then the following matrix will look like 1 1 1 0 -2 -1 0 0 0 by this observation, we can consider that rank cannot be equal to 3(three)., as the third row elements are zeroes(o's) calculate the minors for the following matrix? to calculate minors for the following matrix, first we need to consider the cofactors. a11=1, a12=1, a13=1 a21=0, a22=-2,a23=-1 a31=0, a32=-2,a33=-1 Consider minor as M. consider a 2x2 matrix and atleast if you got the determinant of the following matrix is one non-zero, then the rank is 2. if the determinants of all the corresponding 2x2 matrix is zero, first minor matrix: 1 1 0 -2 solve the determinant for the following matrix: (a11xa22)-(a12xa21) = [1x(-2)]-[{ox1}] = -2 - 0 = -2 we get atleast one non-zero element. hence the rank is considered as 2(two)