Gauss-Jordan Elimination Rules

In summary, the basic rules for using Gauss-Jordan Elimination include being able to multiply an entire row by a nonzero numeral, subtract one row from another, and add or subtract any multiple of one row from another. However, you cannot add or subtract a nonzero numeral to or from a row. Other rules may include swapping two rows. It is important to consult your text or resources, such as the provided link, for a complete list of elementary row operations.
  • #1
Axmann
6
0
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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  • #2
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
 
  • #3
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?
 

Related to Gauss-Jordan Elimination Rules

What is Gauss-Jordan Elimination?

Gauss-Jordan Elimination is a method used to solve systems of linear equations by transforming the system into an equivalent system with simpler equations. It involves using elementary row operations, such as multiplying a row by a nonzero constant, adding one row to another, and exchanging the position of two rows, to manipulate the coefficients of the equations.

What are the steps involved in Gauss-Jordan Elimination?

The steps in Gauss-Jordan Elimination include creating an augmented matrix with the coefficients and constants of the equations, using elementary row operations to simplify the equations, and using back substitution to find the values of the variables. The goal is to transform the matrix into a reduced row-echelon form, where the leading coefficient in each row is 1 and the other elements in the column are 0.

What is the purpose of Gauss-Jordan Elimination?

The purpose of Gauss-Jordan Elimination is to find the solution to a system of linear equations. It can also be used to determine if a system has no solution or infinite solutions. Additionally, it is useful for finding the inverse of a matrix and solving other problems in linear algebra.

What are some common mistakes to avoid when using Gauss-Jordan Elimination?

Some common mistakes to avoid when using Gauss-Jordan Elimination include forgetting to perform an elementary row operation on both sides of the augmented matrix, accidentally multiplying or adding the wrong row, and not using the correct order of operations. It is also important to double-check the final solution by plugging it back into the original equations.

Can Gauss-Jordan Elimination be used for systems with more than two variables?

Yes, Gauss-Jordan Elimination can be used for systems with any number of variables. However, the process can become more tedious and time-consuming as the number of variables increases. In these cases, it may be more efficient to use other methods, such as Gaussian Elimination or Cramer's rule, to solve the system of equations.

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