Exams › JEE Advanced › Maths
Consider the system of linear equations: x - y + 3z = 2, 2x - y + z = 4, x - 2y + az = 3. Which of the following conclusions is correct?
- The system has a unique solution only when a = 0
- The system has a unique solution for all a not equal to 8
- The system has infinitely many solutions when a = 8
- The system has no solution when a = 8
Correct answer: The system has no solution when a = 8
Solution
The determinant D = 0 when a = 8. At a = 8, the augmented matrix is inconsistent (the equations lead to a contradiction), so there is no solution.
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