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Math Help - matrices-solution

  1. #1
    NLG
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    matrices-solution

    Hi, can anyone help me solve this question?

    Which of the matrices are solution of AČ-14A=-48I?

    a) {{-1,1/a},{a,-1}};
    b) {{14,1/a},{a,14}};
    c) {{7,1/a},{a,7}};
    d) {{7,a},{1/a,-48}};
    e) {{-48,0},{0,-48}};

    I replaced the "A" for each of the matrices, but nothing
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    Re: matrices-solution

    Quote Originally Posted by NLG View Post
    a) {{-1,1/a},{a,-1}}; b) {{14,1/a},{a,14}}; c) {{7,1/a},{a,7}}; d) {{7,a},{1/a,-48}}; e) {{-48,0},{0,-48}};
    For the matrix in c):

    A^2-14A=\begin{bmatrix}{50}&{14/a}\\{14a}&{50}\end{bmatrix}-14\begin{bmatrix}{7}&{1/a}\\{a}&{7}\end{bmatrix}=-48\begin{bmatrix}{1}& 0\\{0}&{1} \end{bmatrix}=-48I

    P.S. If you have covered some properties about trace and determinant, then you could reason that the only possible solution is c).
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  3. #3
    NLG
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    Re: matrices-solution

    all right, easy question. Thanks
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