Guassian Elimination (Row reduction) of 3 simultaneous eqn.

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SUMMARY

The discussion centers on solving three simultaneous equations using Gaussian elimination, specifically addressing a student's difficulties in obtaining correct solutions. The student provided an augmented matrix and attempted row operations, including switching rows and performing elimination steps. However, errors in calculations led to incorrect results for x1, x2, and x3. A key mistake identified was in the calculation of R3, where the operation R3 - 2*R1 was incorrectly computed, resulting in erroneous values.

PREREQUISITES
  • Understanding of Gaussian elimination and row reduction techniques.
  • Familiarity with augmented matrices and their manipulation.
  • Basic algebra skills for solving linear equations.
  • Knowledge of matrix operations, including row swapping and scaling.
NEXT STEPS
  • Review Gaussian elimination methods in linear algebra textbooks.
  • Practice solving systems of equations using augmented matrices.
  • Learn about common pitfalls in row operations and how to avoid them.
  • Explore software tools like MATLAB or Python's NumPy for matrix calculations.
USEFUL FOR

Students studying linear algebra, educators teaching Gaussian elimination, and anyone seeking to improve their skills in solving simultaneous equations.

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Homework Statement


I have been given the 3 following simultaneous equations

21kl1ld.jpg


and the question is:
"(a) Solve the equations using Gaussian elimination, showing all your working."

fairly simple topic i know, but i can't get the answer :/

The Attempt at a Solution


Had a few attempts at it.. here's one of them:

Heres my augmented matrix:

34exab9.jpg


I switched Row 1 (R1) with Row 2 (R2)

2ia69ma.jpg


any from there i can work out x1, x2, x3 etc... but i keep getting reidiculous numbers. And when i check them in the 1st set of equations given, they obviously come out to be wrong.

I.e for this attempt i get

x3 = 517/210
x2 = -2297/1230
x1 = -19.408

What am I doing wrong? Any help is much appreciated
Thanks
50
 
Physics news on Phys.org
On your second step where you did R3-2*R1, 26-(2*-21) does not equal 10
 

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