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Math Help - matrix

  1. #1
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    matrix

    let A=[aij],where aij=uivj 1<=i<=n and 1<=j<=n and ui,vj belong to R satisfies A^5=16A find trace(A)
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    Re: matrix

    Hint: Denoting U=\begin{pmatrix}u_1\\ \vdots\\{u_n}\end{pmatrix},\;V=\begin{pmatrix}v_1,  v_2,\hdots,v_n\end{pmatrix} we verify A=UV and A^5=(u_1v_1+\ldots+u_nv_n)^4A=(\textrm{tr}A)^4A
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    Re: matrix

    whats the final answer is it 11
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  4. #4
    MHF Contributor FernandoRevilla's Avatar
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    Re: matrix

    Quote Originally Posted by prasum View Post
    whats the final answer is it 11
    Why?
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