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📐 Mathematics  ·  Determinants  ·  JEE

Gaussian elimination for solving n x n linear systems has time complexity:

Answer: O(n 3 ).

  • A O(n)
  • B O(n<sup>2</sup>)
  • C O(n<sup>3</sup>)
  • D O(2<sup>n</sup>)

Correct answer: C. O(n<sup>3</sup>)

Explanation: Gaussian elimination performs forward elimination (≈n³/3 multiplications) and back substitution (≈n²/2). Dominant term is n³, giving time complexity O(n³). Doubling n increases work roughly 8-fold. Answer: O(n³).

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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