# Gaussian Elimination with Scaled Partial Pivoting

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 R2ïƒ R2 + R3, R3 ïƒ R3 - 2R1, and R4ïƒ 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.