Find rank of Matrix numerical questions

Q1 Find rank of matrix  of matrix A.

          A=  5.     6
              7.     8
                   
      



minor of order 2 matrix is
5*8-7*6
=-2
That is -2 not 0.

so rank of matrix is 2.

Q2 Find rank of matrix A
               A=2.  -4
                -1.   2
                
 




minor of matrix 2*2 is 
=2*2-  -4*-1
=0

so rank of matrix A is 1 because that minor is not zero.

Q3.  Find rank of matrix H

           H= 1.      -1
              3.      -6
             


minor of matrix order 2 is
=-6*1- 3*-1
=-6+3
=-3
so rank of matrix is 2

Q4. Find the max rank of the matrix

           A=1  4
             3  2





rank of matrix =

1*2-4*3=2-12=-10
that is not equal to zero so rank of matrix is 2.

Q5. Find the max  rank of the matrix
                       A=1.     1.      1
                         1.    -1.      0
                         1.     1.      1
                        






First find the minor of 3*3 matrix
=1*(-1-0)-1(1-0)+1(1- -1)
=-1-1+2=0
so 3*3 minor is 0 so 3 is not rank of matrix
now find minor of 2*2 matrix
=1*-1-1*1
=-1-1=-2
so max rank of matrix is 2.