Gaus -jordan elimination compared to cofactor method

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SUMMARY

The discussion centers on the Gauss-Jordan elimination method for finding the inverse of a matrix, specifically the matrix A = [[1, 2, 3], [4, 5, 6], [3, 1, -2]]. The user has successfully performed row operations to achieve a diagonal of 1s and 0s elsewhere but is confused about the next steps to confirm the result aligns with the cofactor matrix calculated as C^T = [[-16/3, 7/3, 1], [26/3, -8/3, 2], [-11/3, 5/3, -1]]. The user seeks clarification on the purpose of the Gauss-Jordan method and its application in finding the inverse matrix.

PREREQUISITES
  • Understanding of matrix operations, including row reduction.
  • Familiarity with the Gauss-Jordan elimination technique.
  • Knowledge of cofactor matrices and their transposition.
  • Basic linear algebra concepts, particularly matrix inverses.
NEXT STEPS
  • Study the complete process of Gauss-Jordan elimination for finding matrix inverses.
  • Learn about the relationship between cofactor matrices and matrix inverses.
  • Explore examples of Gauss-Jordan elimination with different matrices.
  • Investigate the implications of matrix inverses in solving linear equations.
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Students and educators in linear algebra, mathematicians, and anyone seeking to understand matrix inversion techniques using Gauss-Jordan elimination.

latkan
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Hey guys i am stuck with the gaus jordan method of the following matrix.

A = 1 2 3
4 5 6
3 1 -2

For the co factor i worked out the C transpose as:

1/3 (-16 7 3
26 -8 6
-11 5 -3)

The gaus jordan is suppoesed to agree with my final cofactor matrix but i can't seem to understand how to get there?? i have donw the row eliminations to get the diagonal as 1 and the rest as 0.


Add (-4 * row1) to row2

Add (-3 * row1) to row3

Divide row2 by -3

Add (5 * row2) to row3

Divide row3 by -1

Add (-2 * row3) to row2

Add (-3 * row3) to row1

Add (-2 * row2) to row1

But now i don't understand what i have to do now?
 
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It would help if you actually told us what you are doing! The "Gauss-Jordan" method to do what? To find the inverse matrix?
 

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