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

Correct answer: a singleton

Solution

The system of equations has no solution when the determinant of the coefficient matrix is zero, leading to a unique value of 'b' that causes this condition. Thus, the set of distinct values of 'b' is a singleton, indicating only one specific value leads to no solution.

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