if S is the set of distinct values of b for which the following set of linear equations has no solution,then S is

x+Y+z=1

x+ay+z=1

ax+by+z=0

answer-empty set .how?please explain

Here,

             1     1     1

D =       1     a      1       = 0

              a      b      1

For a = 1, the equations become

x + y + z = 1
x + y + z = 1
x + by + z = 0

These equations give no solution for b = 1

Therefore, S is singleton set or empty set