imo class 12 determinants

If |x 2x 3x; 4 5 6; 7 8 9| = 0, then x equals:

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#IMO#Class 12#Mathematics#Determinants#mathematical-reasoning

If |x 2x 3x; 4 5 6; 7 8 9| = 0, then x equals:

  • A. 0 only
  • B. any real number
  • C. 1 only
  • D. −1 only

Answer: B) any real number

Explanation: Taking x common from R1: x × |1 2 3; 4 5 6; 7 8 9|. The remaining determinant is 0, so product is 0 for any x. Hence any real number.

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