JEE Main 2024 Mathematics question
If the system of linear equations x − 2y + z = −4, 2x + αy + 3z = 5, 3x − y + βz = 3 has infinitely many solutions, then 12α + 13β is equal to
Answer: (B)
Solution
For infinitely many solutions the determinants Δ₂ (replacing the y column with the constants) and Δ₃ must vanish. Δ₂ = |[1, −4, 1], [2, 5, 3], [3, 3,
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