Solving systems of equations using Jordan exchanges

In summary, the conversation is about using Jordan exchange to solve a system of equations. The person is asking for clarification on how to determine the values for r and s in the Jordan exchange method. They believe that r represents the row number of the dependent variable and s represents the column number of the independent variable. They also mention a helpful resource for solving the equations using row operations.
  • #1
Robb
225
8
Homework Statement
solve the following system of equations
Relevant Equations
##B_ij = A_{ij} - (A_{rj}/A_{rs})(A_{is})##
##B_{ir} = A_{is}/A_{rs}##
2u + 3v + 3w = 2
+ 5v + 7w = 2
6u + 9v + 8w = 5

##\begin{bmatrix}
2 & 3 & 3 & 2 \\
0 & 5 & 7 & 2 \\
6 & 9 & 8 & 5
\end{bmatrix}##

We have been asked to use Jordan exchange to solve the above equations. Can someone please explain how to determine the values for r, s for the equations above. I believe r is the row number of the dependent variable chosen to be switched with the column for the independent variable, being s. For example, if row 3 and column 3 are chosen, then s = 3 and r = 3. These positions are then used in the homework equations above. Thanks in advance!
 
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Related to Solving systems of equations using Jordan exchanges

1. How do I know when to use Jordan exchanges in solving systems of equations?

Jordan exchanges are typically used when the system of equations involves large numbers or complex coefficients. It is also helpful when one or more of the equations have repeated roots. In general, Jordan exchanges are used to simplify and reduce the size of the system of equations.

2. Can Jordan exchanges be used for any type of system of equations?

Yes, Jordan exchanges can be used for both linear and nonlinear systems of equations. However, it is most commonly used for linear systems with multiple equations.

3. How do I perform Jordan exchanges in solving systems of equations?

To perform a Jordan exchange, you first need to identify the pivot element in the system of equations. This is the coefficient of the leading variable in the first equation. Then, you swap the pivot element with the element in the same column of the last equation. After swapping, you can use the pivot element to eliminate the leading variable in the other equations.

4. What are the benefits of using Jordan exchanges in solving systems of equations?

Jordan exchanges can make the system of equations easier to solve by reducing the number of equations and variables. It also simplifies the system by eliminating the need for fractions or decimals in the coefficients. Additionally, it can help to identify and solve for repeated roots in the system.

5. Are there any limitations to using Jordan exchanges in solving systems of equations?

While Jordan exchanges can be a useful tool in solving systems of equations, they may not always be necessary or efficient. In some cases, other methods such as substitution or elimination may be more suitable. Additionally, Jordan exchanges may not work for all types of equations, such as systems with non-integer coefficients.

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