If S is the set of distinct values of 'b' for which

• Matrices Determinants
• Sets

If S is the set of distinct values of 'b' for which the following system of linear equations
x + y + z = 1
x + ay + z = 1
ax + by + z = 0
has no solution, then S is:

1. an empty set
2. an infinite set
3. a finite set containing two or more elements
4. a singleton

Answer

Here,

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.

The correct option is D.