Exams › JEE Main › Maths

The values of α, for which | 1 3/2 α + 3/2 | | 1 1/3 α + 1/3 | = 0, lie in the interval

1. (-2, 1)
2. (0, 3)
3. (-3, 0)
4. (-3/2, 3/2)

Correct answer: (-3, 0)

Solution

The determinant of the matrix must equal zero for the system to have non-trivial solutions, which occurs when the values of α lead to a specific linear dependency among the rows. Solving the determinant condition reveals that α must lie within the interval (-3, 0) to satisfy this requirement.

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