Gaus -jordan elimination compared to cofactor method

In summary, the conversation is about being stuck with the Gauss-Jordan method for a given matrix and trying to get the diagonal as 1 and the rest as 0. The person has already done some row eliminations and is now unsure of what to do next. They also mention needing help with understanding what they are supposed to do.
  • #1
latkan
5
0
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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  • #2
It would help if you actually told us what you are doing! The "Gauss-Jordan" method to do what? To find the inverse matrix?
 

What is the difference between Gauss-Jordan elimination and cofactor method?

Gauss-Jordan elimination and cofactor method are two different techniques used to solve systems of linear equations. Gauss-Jordan elimination involves performing row operations on a matrix to simplify it into a reduced row-echelon form, while cofactor method uses determinants and matrix inverses to find the solution.

Which method is more efficient, Gauss-Jordan elimination or cofactor method?

In general, Gauss-Jordan elimination is considered to be more efficient as it involves fewer steps and calculations compared to cofactor method. However, the efficiency of each method may vary depending on the specific system of equations being solved.

Can either method be used to solve any system of linear equations?

Yes, both Gauss-Jordan elimination and cofactor method can be used to solve any system of linear equations. However, the suitability of each method may depend on the size and complexity of the system.

What are the advantages of using Gauss-Jordan elimination over cofactor method?

One advantage of Gauss-Jordan elimination is that it can easily handle systems of equations with any number of variables, while cofactor method may become more complex for larger systems. Additionally, Gauss-Jordan elimination produces a unique solution, while cofactor method may result in multiple solutions or no solution at all.

Are there any situations where cofactor method may be preferred over Gauss-Jordan elimination?

Cofactor method may be preferred over Gauss-Jordan elimination in situations where the coefficient matrix is sparse (contains many zeros) or when the system of equations has a special structure, such as a symmetric matrix. In such cases, cofactor method may require fewer calculations and be more efficient.

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