JEE Main 2024 Mathematics question

Consider the system of linear equations x + y + z = 5, x + 2y + λ²z = 9, x + 3y + λz = μ, where λ, μ ∈ ℝ. Then, which of the following statement is NOT correct?

(A)System has unique solution if λ ≠ 1 and μ ≠ 13Correct
(B)System is inconsistent if λ = 1 and μ ≠ 13
(C)System has infinite number of solutions if λ = 1 and μ = 13
(D)System is consistent if λ ≠ 1 and μ = 13

Answer: (A)

Solution

The determinant of the coefficients is Δ = −(2λ + 1)(λ − 1) (up to sign). So the system has a unique solution only when λ ≠ 1 and λ ≠ −1/2. For λ = −1/2 the equations reduce to x + y + z = 5, 4x + 8y + z = 36, 2x +

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Question ID VK-016997