Hello From Linear Algebra

A has m equations with n unknowns.
eq: a(i,1)x(1) + a(i,2)x(2) + .... + a(i,n)x(n) = d(i) ; 1 <= i <= m
A already solve it.
Now A wants B to set values for n unknowns which will true for each equation if possible.
What is the probability that A's solution and B's solution are exactly same?"

Ans:
For set of equation there will be 3 type of ans,

1. Set of equation has no solution
   ex: x + y = 2
x + y = 5
2. Set of equation has only one solution
   ex: x + y = 3
x - y = 2
3. Set of equation has inf solution
   ex: x + y = 3

For type 1 and 2 probability should be 1 (1/1) and for type 3 probability is 0 (1/inf)