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    Gaussian Elimination Count

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    Please help with solving the following question regarding Gaussian eliminations to a system.

    The system
    [see the attachment for the matrix and equation]

    Where a_ij = 0 whenever i-j >= 2

    Do an operation count of MD (Multiplications/Division) and AS (Addition/Subtraction) when using Gaussian elimination to solve the system.

    Count [A] -> [U]
    Compare the result with the count of Gaussian elimination for general matrix:
    SA [A] - [U] = [see the attachment for the equation]
    MD [A] -> [U] = [see the attachment for the equation]

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    https://brainmass.com/math/combinatorics/gaussian-elimination-count-522240

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    Solution Preview

    Compare means to mention the similarities between the two answers and it also could mean to say which one is larger and why.

    1. Let's start with MD:

    The answer for MD: n(n+1)/2 - 1 or (n-1)(n+2)/2

    For the general matrix, MD: n(n^2-1)/3

    which factors to n(n+1)(n-1)/3 since n >=1 the general answer ...

    Solution Summary

    This solution provides a comparison of the operation count for different types of matrices; one matrix is general, and the other has specific elements zeroed out.

    $2.19