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Math Help - Determinants

  1. #1
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    Determinants

    Hi

    can anyone help with the last 3 determinants( exc: 8,9,10)
    from this page

    http://myweb.polyu.edu.hk/~majleung/...terminants.pdf

    Thank you!
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  2. #2
    MHF Contributor

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    Quote Originally Posted by benus View Post
    Hi

    can anyone help with the last 3 determinants( exc: 8,9,10)
    from this page

    http://myweb.polyu.edu.hk/~majleung/...terminants.pdf

    Thank you!
    Look at the righthand side of each of those.
    Do you have a theorem that says
    \left|\begin{array}{cccc}a_1+ x & x & \cdot\cdot\cdot & x \\ x & a_2+ x & \cdot\cdot\cdot & x\\ \cdot & \cdot & \cdot & \cdot \\x & x & \cdot\cdot\cdot a_n+ x\end{array}\right| = a_1a_2\cdot\cdot\cdot a_n+ (a_1+ a_2+ \cdot\cdot\cdot+ a_n)x?

    If not, could you prove it by induction on n?
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