imo class 12 determinants

An examination has 3 subjects. A student's scores are represented by an equation system. If |A| ≠ 0, how many sets of scores satisfy the system?

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An examination has 3 subjects. A student's scores are represented by an equation system. If |A| ≠ 0, how many sets of scores satisfy the system?

  • A. Zero
  • B. One unique set
  • C. Three sets
  • D. Infinite sets

Answer: B) One unique set

Explanation: A non-zero determinant implies a non-singular matrix, meaning the system of equations has exactly one unique solution.

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