IIT JAM
Thanu dharshani. t. t Asked a Question
July 13, 2021 5:04 ampts 30 pts
  • IIT JAM
  • Mathematics (MA)

Let ae m,, (c). then a is diagonalizable if and only if: a) a = 0. (b) a = i. (c) n =2. d) none of the other three options.

Let AE M,, (C). Then A is diagonalizable if and only if: a) A = 0. (b) A = I. (c) n =2. d) None of the other three options.
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  • Ankur Rao
    feel free to ask if you have any doubts.
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  • Thanu dharshani. t. t
    but matrix with trace 0 is diagonalisable?
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    Ankur Rao
    yes it can be possible because let zero matrix or take a diagonal non zero matrix whose trace is zero then it will be diagonalizable
  • Ankur Rao thankyou
    option (a) is true only. a) as if A is zero matrix then the above matrix will also be zero and we know zero matrix is diagonal matrix contain zero in diagonals. so it will be true...
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