IIT JAM
Shwet goyal 1 Asked a Question
October 29, 2021 1:04 ampts 30 pts
  • IIT JAM
  • Mathematics (MA)

Let f(x) be the minimal polynomial of the 5 x 5 matrix o 00 1 0 1 0 0 0 0 a = 0 1 0 3 0d 0 0 2 0 6 0 0 0 4 0 then rank of the matrix f(a) is

Let f(x) be the minimal polynomial of the 5 x 5 matrix O 00 1 0 1 0 0 0 0 A = 0 1 0 3 0D 0 0 2 0 6 0 0 0 4 0 Then rank of the matrix f(A) is
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  • Shwet goyal 1
    ok sir.
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  • Shwet goyal 1
    sir, yaha par minimal polynomial ki rank puchi thi. Ye toh normal form hai.
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    Navdeep goyal 1
     A has distinct n non-zero eigen values in an extension field of F, μ is the characteristic polynomial of A. Hence deg μ=n= rank A
  • Navdeep goyal 1 thankyou
    4
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