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IPMAT Indore 2022 - QA (MCQ) Q20 Explanation
December 27, 2024
Explanation:
(C)
Suppose a, b and c are integers such that a > b > c > 0, and A = [ 𝑎 𝑏 𝑐 𝑏 𝑐 𝑎 𝑐 𝑎 𝑏 ] Then the value of the determinant of A
Determinant ∆ = a (bc-a^2) – b (b^2 - ac) + c (ab-c^2) = 3 abc− a^3− b^3− c^3
Assuming a = 3, b = 2 and c = 1 (As given that a > b > c > 0)
∆ = (3 × 3 × 2 × 1) - 3^3 - 2^3 -1^3 = 18 - 38 = -20, which is negative
So, ∆ will always be negative.