Prachi Kashyap posted an Question
February 02, 2022 • 14:07 pm 30 points
  • IIT JAM
  • Mathematics (MA)

60 57. let a =a :a er be a nilpotent matrix j jo:9 of indexr. if a, is replaced by a -1; vi =l to 9, then the rank of new matrix so obtained is

60 57. Let A =a :a eR be a nilpotent matrix j Jo:9 of indexr. If a, is replaced by a -1; Vi =l to 9, then the rank of new matrix so obtained is

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    Kanika goswami 1 best-answer

    as it is nilpotent matrix so all eigen values of this are 0 and after replacing aii to aii-1 we get all eigen values are -1 . i.e., we get an invertible matrix so rank of new matrix is 9.

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