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###### Shwet Goyal posted an Question
October 29, 2021 • 01:04 am 30 points
• 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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ok sir.

• ##### Shwet goyal 1

sir, yaha par minimal polynomial ki rank puchi thi. Ye toh normal form hai.

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

understand

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