Solving Systems of Linear Equations (Echelon Matrices)

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SUMMARY

The discussion focuses on solving systems of linear equations using Row Echelon Operations and Gaussian elimination. The correct solution to the given system is identified as x = 1, y = 1, z = 2, w = −3. A common mistake highlighted involves incorrect calculations when performing row operations, specifically the addition of 18 times row 3 to row 4, where the last term should be calculated as 16/14*18 instead of 16/4*18. This emphasizes the importance of accuracy in row operations during the elimination process.

PREREQUISITES
  • Understanding of Row Echelon Form
  • Proficiency in Gaussian elimination techniques
  • Familiarity with matrix operations
  • Basic algebra skills for solving linear equations
NEXT STEPS
  • Practice additional problems involving Row Echelon Form
  • Study advanced techniques in Gaussian elimination
  • Learn about matrix inverses and their applications
  • Explore software tools for matrix calculations, such as MATLAB or Python's NumPy
USEFUL FOR

Students studying linear algebra, educators teaching systems of equations, and anyone looking to improve their skills in matrix operations and Gaussian elimination.

DiamondV
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Homework Statement


find the general solution of the given system of equations:
http://puu.sh/ncKaS/57a333f5b9.png

Homework Equations


Row Echelon Operations

The Attempt at a Solution


http://puu.sh/ncKcm/3e2b2bd5ab.jpg

The correct answer given is x = 1, y = 1, z = 2, w = −3

I have done quite a few of these now around 5-6 and have gotten 3 correct. I don't know what my mistake with this one is. We are using Gaussian elimination.[/B]
 
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When you add 18 times r3 to r4, the last term of row 3 is 16/14*18 not 16/4*18
 
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Gianmarco said:
When you add 18 times r3 to r4, the last term of row 3 is 16/14*18 not 16/4*18

Ahhh. Thanks soo much.
 

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