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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.
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Augmented Matrix a 1 x +b 1 y +c 1 z =d 1 a 2 x +b 2 y +c 2 z
=d 2 a 3 x +b 3 y +c 3 z =d 3 System of Equations Augmented
Matrix
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Example System of Equations Augmented Matrix
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Elementary Row Operations 1.Interchanging two rows. 2.Adding
one row to another row, or multiplying one row by a constant first
and then adding it to another. 3.Multiplying a row by any constant
different from zero.
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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.
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Identity Matrix Identity Matrix for a 3 x 3 Identity Matrix for
a 4 x 4
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Solving the System 1. Write as an augmented Matrix2. Switch row
1 with row 2
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3. Multiply Row 1 by -3 and add Row 2 R 1 (-3) -33-6-12 + 32-1
3 05-7 -9 R2R2 R2R2 R 1 (-3) + R 2 R 2
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4. Multiply Row 1 by -2 and add Row 3 R 1 (-2) -22-4-8 + 23-1 3
05-5 -5 R3R3 R3R3 R 1 (-2) + R 3 R 3
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5. Switch Row 2 with Row 3 6. Multiply Row 2 by 1/5 R 2 (1/5 )
R 2 R 2 R 3
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7. Add Row 2 to Row 1 R 1 + R 2 R 1 8. Multiply Row 2 by -5 and
Add Row 3 R 2 (-5) + R 3 R 3
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10. Add Row 3 and Row 2 9. Multiply Row 3 by -1/2 R 3 ( -1/2 )
R 3 R 3 + R 2 R 2
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Final Answer 11. Multiply Row 3 by -1 and add Row 1 R 3 (-1) +
R 1 R 1
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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