if No of variables = 3
and rank of matrix (A) = 2
No of linear independent solution : 3-2 = 1
which means if a equation is like that
x + 3y + 2z = 0
-7y + 8z = 0
therefore Y = (8/7) Z , X = (10/7) Z
let Z = c
Y = (8/7)c , X = (10/7)C
for any arbitrary value of C we can get X and Y
therefore no of independent solution = 1 from which we can derive infinite solution
Similarly if
if No of variables = 3
and rank of matrix (A) = 1
No of linear independent solution : 3-2 = 1