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Gaussian elimination and Gauss-Siedel

Please see attached pdf file with 4 problems on Gauss Elimination as well as Gauss-Siedel.

Solution Preview

There are four problems:
Question 1:
12x - 8.6y = 52.16
5.3x + 17y = 114.55
Writing the augmented matrix of the system,
(A, b) =
Dividing R1by 12 and R2 by 5.3 gives
~
~ (R2 - R1)
~ (R2/ )
This is the final RREF form of the augmented matrix.
Working the way up, y = 4.4
And x - 0.7166666667y = 4.3466666667, which gives x = 0.7166666667*4.4 + 4.3466666667 = 7.5
Therefore, the solution set is (7.5, 4.4). This system does not seem to be highly sensitive to changes in the values on the right hand side, because the final solution is only one place after decimal.
Question 2:
(a) The starting matrix system is:
Matrix Three bi's Checksum
1.7 2.3 4.7 10.5 11.03 10.5 40.73
3.9 1.2 -2.1 3 2.85 3 11.85
-3 5.1 3 4.9 4.9 5.15 20.05

Dividing R1 by 1.7, R2 by 3.9, and R3 by -3 gives
Matrix Three bi's Checksum
1 1.352941 2.764706 6.176471 6.488235 6.176471 23.958824
1 0.307692 -0.53846 0.769231 0.730769 0.769231 3.0384615
1 -1.7 -1 -1.63333 -1.63333 -1.71667 -6.683333
R2 - R1 and R3 - R1 gives:
Matrix Three ...

Solution Summary

The solution shows how to solve systems of equations using Gaussian elimination and Gauss-Siedel.

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