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Learn how to solve a system of linear equations using the Gauss Jordan Elimination algorithm, which reduces an augmented matrix to the reduced row echelon form. See the steps, the conditions, and the examples of this method with solutions and practice questions.
The Gauss-Jordan elimination method refers to a strategy used to obtain the reduced row-echelon form of a matrix. The goal is to write matrix \(A\) with the number \(1\) as the entry down the main diagonal and have all zeros above and below.
Learn how to use row reduction to solve systems of linear equations and compute matrix inverses. See examples, definitions, and explanations of Gauss-Jordan elimination and its variations.
- Write the following system as an augmented matrix. \[\begin{array}{l} 2 x+3 y-4 z=5 \\ 3 x+4 y-5 z=-6 \\ 4 x+5 y-6 z=7. \end{array}\nonumber \]
- For the following augmented matrix, write the system of equations it represents. \[\left[\begin{array}{ccccc} 1 & 3 & -5 & | & 2 \\
- Solve the following system by the elimination method. \[\begin{array}{l} x+3 y=7 \\ 3 x+4 y=11. \end{array} \nonumber \] Solution. We multiply the first equation by – 3, and add it to the second equation.
- Solve the following system from Example 3 by the Gauss-Jordan method, and show the similarities in both methods by writing the equations next to the matrices.
The Gauss Jordan elimination algorithm and its steps. With examples and solved exercises. Learn how the algorithm is used to reduce a system to reduced row echelon form.
Sep 17, 2022 · The following function is a basic implementation of the Gauss-Jorden algorithm to an (m,m+1) augmented matrix: This page titled 7.2: Introduction to Gauss Jordan Elimination is shared under a CC BY-NC 4.0 license and was authored, remixed, and/or curated by Dirk Colbry via source content that was edited to the style and standards of the ...
Learn how to use Gauss-Jordan elimination to solve systems of linear equations and find the rank of a matrix. See examples, history and applications of the method in tomography and celestial mechanics.
