Anonymous posted an Question
September 19, 2020 • 12:27 pm 30 points
  • CSIR NET
  • Mathematical Sciences

10. v is a finite dimensional vector space and p is a non-zero linear map from v to v such that p? = p. which of the following statements is not necessarily tru

10. V is a finite dimensional vector space and P is a non-zero linear map from V to V such that P? = P. Which of the following statements is not necessarily true? (a) Ran(P) n Ran(I - P) = {0}. (b) (I- P = I- P. (c) P is diagonalisable. (d) P is invertible.

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    Satpal singh Best Answer

    see the attachment so option D is not necessarily true. option B and C are direct results for idempotent matrix

    cropped18937215363607452.jpg
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    see these

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