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Assertion: a matrix with n distinct eigenvalues is diagonalisable. Reason: distinct eigenvalues are necessary for n independent eigenvectors.

  • A.the assertion is true but the reason overstates the requirement
  • B.both the assertion and the reason are true and the reason explains the assertion
  • C.both the assertion and the reason are true but the reason does not explain the assertion
  • D.both the assertion and the reason are false

Answer: A

Distinct eigenvalues do guarantee independence and so make the matrix diagonalisable, but they are sufficient rather than necessary. A repeated eigenvalue may still supply enough independent eigenvectors, as the identity matrix shows.

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