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If T : V → V be a linear operator for dim V = n and T has n distinct eigenvalues then
  • a)
    T must be invertible.
  • b)
    T must be diagonalizable.
  • c)
    T must be invertible as well as diagonalizable.
  • d)
    T is not diagonalizable.
Correct answer is option 'B'. Can you explain this answer?
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If T : V → V be a linear operator for dim V = n and T has n disti...
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If T : V → V be a linear operator for dim V = n and T has n disti...
N distinct eigen values means diagonalizable. If one eigen value is zero, it is not invertible
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If T : V → V be a linear operator for dim V = n and T has n distinct eigenvalues thena)T must be invertible.b)T must be diagonalizable.c)T must be invertible as well as diagonalizable.d)T is not diagonalizable.Correct answer is option 'B'. Can you explain this answer?
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