Gauss-Jordan Elimination Rules

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SUMMARY

The discussion focuses on the fundamental rules of Gauss-Jordan Elimination, a method used in linear algebra for solving systems of equations. Key operations include multiplying an entire row by a nonzero numeral, subtracting one row from another, and swapping two rows. It is explicitly stated that adding or subtracting a nonzero numeral to or from a row is not permitted. For further clarification, users are directed to refer to the Wikipedia page on elementary matrices.

PREREQUISITES
  • Understanding of linear algebra concepts
  • Familiarity with matrix operations
  • Knowledge of elementary row operations
  • Basic skills in manipulating equations
NEXT STEPS
  • Study the complete list of elementary row operations in linear algebra
  • Learn about the applications of Gauss-Jordan Elimination in solving linear systems
  • Explore the concept of elementary matrices in depth
  • Practice solving systems of equations using Gauss-Jordan Elimination
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Students of linear algebra, educators teaching matrix theory, and anyone looking to master the Gauss-Jordan Elimination method for solving systems of equations.

Axmann
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Can someone please explain the basic rules that must be adhered to when using Gauss-Jordan Elimination? I've been having some difficulty with it because apparently I keep doing things that you aren't allowed to do.

So far, I know only the following:

-You CAN multiply an entire row by a nonzero numeral
-You CAN subtract one row from another
-You CANNOT add or subtract a nonzero numeral to (or from) a row

What other rules are there?
 
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Axmann said:
Can someone please explain the basic rules that must be adhered to when using Gauss-Jordan Elimination? I've been having some difficulty with it because apparently I keep doing things that you aren't allowed to do.

So far, I know only the following:

-You CAN multiply an entire row by a nonzero numeral
-You CAN subtract one row from another
-You CANNOT add or subtract a nonzero numeral to (or from) a row

What other rules are there?

If the elementary row operations aren't listed in your text, look here:

http://en.wikipedia.org/wiki/Elementary_matrix
 
Axmann said:
Can someone please explain the basic rules that must be adhered to when using Gauss-Jordan Elimination? I've been having some difficulty with it because apparently I keep doing things that you aren't allowed to do.

So far, I know only the following:

-You CAN multiply an entire row by a nonzero numeral
-You CAN subtract one row from another
Add or subtract any multiple of one row from another,
Swap two rows.

-You CANNOT add or subtract a nonzero numeral to (or from) a row

What other rules are there?
 

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