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The number of real values of λ, such that the system of linear equations 2x − 3y + 5z = 9 x + 3y − z = −18 3x − y + (λ^2 − λ)z = 16 has no solution, is

1. 0
2. 1
3. 2
4. 4

Correct answer: 1

Solution

The system of equations has no solution when the determinant of the coefficient matrix is zero and the augmented matrix has a different rank. In this case, there is exactly one value of λ that causes the determinant to be zero, indicating that the system is inconsistent.

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