I've got a solution for this problem. I just wanna confirm this as my text book
doesn't provide answers for all questions.
Let A be a 5x4 matrix with real entries such that the space of all solutions of the linear system
AX^{t} = is given by
{ }.
Then the rank of the matrix A is
a) 4 b) 3 c) 2 d)1
SOLUTION:
My argument is as follows.
i) The rank of the matrix A is 4 atmost.
ii) Since the solution matrix has one free variable, the rank cannot be 4 and has to be 4-1 = 3.
Let me know if there is a flaw in my argument.