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    Gaussian Elimination with Scaled Partial Pivoting

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    Please see attached problem (both Word and pdf version attached).

    Solve the system

    3x1 13x2 | 9x3 | 3x4 = 19
    6x1 | 4x2 | x3 18x4 = 34
    6x1 - 2x2 + 2x3 + 4x4 - 16
    12x1 - 8x2 + 6x3 + 10x4 - 26

    by hand using scaled partial pivoting. You may only do the operations on rows that are permitted in Algorithm 6.3 You should never multiply a row by a constant for any reason. Interchange rows as necessary rather than use the NROW arrow. Justify all row interchanges and write out the transformed matrix after you finish working on each column.

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    Solution Preview

    Gaussian Elimination with Scaled Partial Pivoting

    Writing the augmented matrix of the system:

    Keeping R1 unchanged and R2R2 + R3, R3  R3 - 2R1, and R4R4 - 4R1 gives:

    Keeping ...

    Solution Summary

    This provides an example of using Gaussian elimination with scaled partial pivoting with copies of work in both a Word and PDF document.