If `S` is the set of distinct values of `' b` for which the following system of linear equations `x+y+z=1` `x+a y+z=1` `a x+b y+z=0` has no solution, then `S` is :
(1) a finite set containing two or more elements
(2) a singleton set
(3) an empty set
(4) an infinite set

Explanation

To solve the problem, we need to determine the set \( S \) of distinct values of \( b \) for which the given system of linear equations has no solution. The equations are:

1. \( x + y + z = 1 \) (Equation 1)
2. \( x + ay + z = 1 \) (Equation 2)
3. \( ax + by + z = 0 \) (Equation 3)

### Step 1: Write the coefficient matrix and find its determinant

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