1. Larger Systems of Linear Equations and Matrices
Section 6.2
Larger Systems of Linear Equations and Matrices
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Gauss-Jordan Method
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20. Gauss-Jordan Elimination
With Gaussian elimination, elementary row operations are applied to a matrix to obtain a (row-equivalent) row-echelon form of the matrix.
A second method of elimination, called Gauss-Jordan elimination, continues the reduction process until a reduced row-echelon form is obtained.
This procedure is demonstrated in Example 8.

21. Example– Gauss-Jordan Elimination
Use Gauss-Jordan elimination to solve the system x – 2y + 3z = 9
–x + 3y = –4
2x – 5y + 5z = 17
Solution:
The row-echelon form of the linear system can be obtained using the Gaussian elimination. .

22. Example – Solution
cont’d
Now, apply elementary row operations until you obtain zeros above each of the leading 1’s, as follows.
Perform operations on R1
so second column has a
zero above its leading 1.
Perform operations on R1
and R2 so third column has
zeros above its leading 1.

23. Example – Solution
The matrix is now in reduced row-echelon form. Converting back to a system of linear equations, you have
x = 1
y = –1.
z = 2
Now you can simply read the solution, x = 1, y = –1, and z = 2 which can be written as the ordered triple(1, –1, 2).
cont’d

24. Reduced Row Echelon Form : Gauss-Jordan Method
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27. The system is inconsistent.
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