imo class 12 determinants

A student solved a 3×3 matrix using Cramer's rule. If Dx = 0, Dy = 0, Dz = 0 and D ≠ 0, what is the solution?

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A student solved a 3×3 matrix using Cramer's rule. If Dx = 0, Dy = 0, Dz = 0 and D ≠ 0, what is the solution?

  • A. No solution
  • B. x=1, y=1, z=1
  • C. Infinite solutions
  • D. x=0, y=0, z=0

Answer: D) x=0, y=0, z=0

Explanation: By Cramer's rule, x = Dx/D = 0/D = 0. Similarly, y = 0 and z = 0. This is the trivial solution.

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