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When is Cramer's rule applicable to a system of linear equations?

  • A.when there are more equations than unknowns
  • B.when the coefficient determinant is non-zero
  • C.when the coefficient determinant is zero
  • D.when the system is homogeneous

Answer: B

A non-zero coefficient determinant guarantees a unique solution, each unknown being a ratio of two determinants. When it vanishes the rule fails and the rank criteria must be used to decide between no solution and infinitely many.

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