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Let S be the set of all real values of k for which the system of linear equations x + y + z = 2 2x + y − z = 3 3x + 2y + kz = 4 has a unique solution. Then S is

1. an empty set
2. equal to R − {0}
3. equal to {0}
4. equal to R

Correct answer: equal to R − {0}

Solution

The system of equations has a unique solution when the determinant of the coefficient matrix is non-zero. For the given equations, this condition is satisfied for all values of k except k = 0, leading to the conclusion that the set S consists of all real numbers except zero.

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