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Let T : be a linear operator having n distinct eigenvalues. Then
  • a)
    T is invertible
  • b)
    T is invertible as well as diagonalizable.
  • c)
    T is not diagonalizable.
  • d)
    T is diagonalizable
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
Let T : be a linear operator having n distinct eigenvalues. Thena)T i...
If one from the distinct eigenvalues is zero. Then it will be singular and hence, not invertible but T is necessarily diagonalizable.
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Let T : be a linear operator having n distinct eigenvalues. Thena)T is invertibleb)T is invertible as well as diagonalizable.c)T is not diagonalizable.d)T is diagonalizableCorrect answer is option 'D'. Can you explain this answer?
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