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Math Help - matrix question help

  1. #1
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    matrix question help

    Consider a sequence of real numbers r1, r2 .... rn such that no two numbers are equal. Using these numbers, we create ( N x N) square matrix R such that the ( i, j)-th element of R is given by

    ai, j = rk, where k = min(i, j), i = 1,2,...., N; j = 1,2,....,N.

    Write the elements of matrix R in terms of real numbers r1,r2,....,rn. Clearly show at least the top 4 x 4 and all the elements on the four corners.

    And is this a symmetric matrix?
    Attached Thumbnails Attached Thumbnails matrix question help-screenshot_2012-09-01-13-16-12-1.png  
    Last edited by LaVsy; August 31st 2012 at 10:18 PM.
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  2. #2
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    Re: matrix question help

    need help anyone ?
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  3. #3
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    Re: matrix question help

    This is how the matrix will look.
    \left( \begin{array}{cccccccc}r_1 & r_1 & r_1 & r_1& r_1&...&...&r_1\\r_1 & r_2 & r_2 & r_2& r_2&...&...&r_2\\r_1 & r_2 & r_3 & r_3& r_3&...&...&r_3\\r_1 & r_2 & r_3 & r_4& r_4&...&...&r_4\\r_1 & r_2 & r_3 & r_4& r_5&...&...&r_5\\... & ... & ... & ... & ... & ...& ... & ...\\... & ... & ... & ... & ... & ...& ... & ...\\r_1 & r_2 & r_3 & r_4 & r_5 & ...& ... & r_N\\ \end{array} \right)

    The argument goes like this for the first row and column the index of the elements will be a_{1k} and a_{k1} respectively so for all these elements we have r_1. Now consider the sub-matrix by removing the first row and first column which is (N-1)x (N-1) but the index of the elements will be starting from 2 and repeat the argument.

    Now you can answer the second question if the matrix is symmetric or not?
    ~Kalyan.
    Last edited by kalyanram; September 2nd 2012 at 08:57 AM.
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    Re: matrix question help

    Am I right to say that

    R^(T) = r1 r1 r1 r1
    r1 r2 r2 r2
    r1 r2 r3 r3
    r1 r2 r3 r4

    So they are SYMMETRIC.

    Am I correct?
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    Last edited by LaVsy; September 3rd 2012 at 11:43 PM.
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  5. #5
    Member kalyanram's Avatar
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    Re: matrix question help

    You are correct. The matrix is Symmetric.
    ~Kalyan.
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  6. #6
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    Re: matrix question help

    thanks for the solutions posted. Do you have the solutions for the remaining parts? I am taking the module TG1401 currently struggling to do CA1.
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