How to solve this linear equations using three-digit rounding for both the resul

Question

How to solve this linear equations using three-digit rounding for both the results and multiplier in part (a)?

what's the solution for b and c also?

3.3330x 15920x2 +10.333x3 7953 2.2220x 16.7 10x2 +9.6120x3 0.965. 1.56 11x1 5.1792 1.6855x 2.714 with actual solution: ll, 0.5 a. Use Gaussian elimination and three-digit rounding arithmetic to solve the above linear systems, and compare the approximations to the actual solution. b. Repeat the exercise using Gaussian elimination with partial pivoting. c. Repeat the exercise using Gaussian elimination with scaled pivoting.

Explanation / Answer

3.3330x1+15920x2+10.333x3=7952 .........equation 1
2.2220x1+16.710x2+9.6120x3=0.965.........equation2
-1.5611x1+14.2x2-1.6855x3=2.714..............equation3

multiply eq 2 by 1.5611 and eq 1 by 2.2220 we get,
3.468x1+26.085x2+15.005x3=1.506
-3.468x1+31.552x2-3.745x3=6.030

adding above 2 equations,
57.637x2+11.26x3=7.536
x2=(7.536-11.26x3)/57.637..............equation4

similarly
multiply eq 3 by 16.710 and eq 3 by 14.2 and adding those two we get,

x3=(46.7212-5.47x1)/108.326..............equation5

solving equaion 1,4,5
ie,by putting value of x2 and x3 in the form of x1 in equation 1,we get value of x1

x1=45.08

substituting value of x1 in eq 4 and eq 5 we get

x2=.4911

and

x3=-1.845

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