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what is the characteristics polynomial and minimal polynomial of A and B?

Discussion in 'Mathematics' started by jasmine, Oct 8, 2018.

  1. jasmine

    jasmine Guest

    what is characteristics polynomial and minimal polynomial of A and B?

    $A=\begin{pmatrix} a & 1 & 0 & 0 \\ 0 & a & 0 & 0 \\ 0 & 0 & a & 0 \\ 0 & 0 & 0 & a\end{pmatrix},B=\begin{pmatrix} a & 1 & 0 & 0 \\ 0 & a & 0 & 0 \\ 0 & 0 & a & 1 \\ 0 & 0 & 0 & a\end{pmatrix}$

    My attempt : for $A$) , $ch_A(x) = (x-a)^4$ , $m_A = (x-a)^2(x-a)$

    for $B)$ $ch_B(x) = (x-a)^4$ , $m_B = (x-a)^2(x-a)^2$

    where $ch$ and $m$ denote the characteristics nad minimial polynomial

    is my answer is correct or not ???

    Any hints/solution will be apprciated

    thanks u

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