Solve Linear System with Gaussian Elimination

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SUMMARY

The discussion focuses on solving a linear system using Gaussian elimination with 3-digit rounding arithmetic. The specific linear equations provided are: 3.3330x_1 + 15920x_2 + 10.333x_3 = 7953, 2.2220x_1 + 16.710x_2 + 9.6120x_3 = 0.965, and -1.5611x_1 + 5.1792x_2 - 1.6855x_3 = 2.714. A recommended online tool, Greg Thatcher's Gauss-Jordan elimination website, is suggested for step-by-step guidance, although users are advised to stop at the Gaussian elimination stage. The user is also tasked with comparing their results to the known solutions: x_1 = 1, x_2 = 0.5, and x_3 = -1.

PREREQUISITES
  • Understanding of Gaussian elimination
  • Familiarity with 3-digit rounding arithmetic
  • Basic knowledge of linear algebra concepts
  • Ability to interpret matrix representations of linear systems
NEXT STEPS
  • Practice solving linear systems using Gaussian elimination
  • Explore the Gauss-Jordan elimination method for deeper understanding
  • Learn about matrix representation and operations in linear algebra
  • Investigate numerical stability and rounding errors in computations
USEFUL FOR

Students learning linear algebra, educators teaching Gaussian elimination, and anyone seeking to improve their problem-solving skills in mathematics.

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Homework Statement



Hey everyone! I was handed this question in class without being taught how to do it! The text is supposed to be helpful but it is just confusing.

Using Gaussian elimination and 3-digit rounding arithmetic, solve the following linear system:

3.3330x_1 +15920x_2 +10.333x_3 = 7953
2.2220x_1 +16.710x_2 +9.6120x_3 = 0.965
-1.5611x_1 +5.1792x_2 -1.6855x_3 = 2.714

I'm then supposed to compare it to the actual solutions of x_1 = 1, x_2 = 0.5 and x_3 = -1 but I believe I know how to do that. :)

If there is anyway you can let me know how to do the above problem I'd really appreciate it! I want to learn this and the textbook is not clear at all.
 
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Note that the above link takes it a step further with Gauss-Jordan elimination.

Just simply quit when you have reached the requirements for regular Gaussian elimination.
 

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