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📐 Mathematics  ·  Determinants  ·  JEE

The system x + ky + z = 0, kx + y + z = 0, x + y + kz = 0 has a non-trivial solution when:

Answer: k = 1 or k = −2.

  • A k = 1 or k = −2
  • B k = 0 or k = 1
  • C k = −1 or k = 2
  • D k = 2 only

Correct answer: A. k = 1 or k = −2

Explanation: The coefficient determinant is −(k − 1)²(k + 2), which vanishes at k = 1 or k = −2.

Concept context

Evaluation of determinants, cofactors, adjoint, inverse of matrix, Cramer's rule and area applications. Always in board and JEE.

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