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Gauss-Jordan Matrix Elimination

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Gauss-Jordan Matrix Elimination

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    1. Gauss-Jordan Matrix Elimination Brought to you by Tutorial Services The Math Center

    2. Gauss-Jordan Matrix Elimination A method that can be used to solve systems of linear equations involving two or more variables. To do so, the system must be changed first, to an augmented matrix.

    3. Augmented Matrix a1 x +b1 y +c1 z =d1 a2 x +b2 y +c2 z =d2 a3 x +b3 y +c3 z =d3

    4. Example

    5. Elementary Row Operations Interchanging two rows. Adding one row to another row, or multiplying one row by a constant first and then adding it to another. Multiplying a row by any constant different from zero.

    6. Gauss-Jordan Matrix Elimination Goal In order to solve the system of equations, a series of steps needs to be followed using the elementary row operations. The reduced matrix should end up being the identity matrix.

    7. Identity Matrix

    8. Solving the System

    15. Gauss Jordan Handouts and Links Gauss Jordan Method Handout Adding and Subtracting Matrices Workshop Adding and Subtracting Matrices Handout Multiplying Matrices Workshop Multiplying Matrices Handout Inverse Matrix Handout

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