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Example of Gauss-jordan:
For a 2×2 system, this would results
and for a 3 × 3 system,
Note that the resulting diagonal form does not involve the right-most column.
For illustration, the 2 × 2 system, forward elimination results the matrix:
Now, to carry on with back elimination, we require a 0 in the a12 position.
Therefore, the solution is x1 = 4; -2x2 = 2 or x2 = -1.
Here is an illustration of a 3× 3 system:
In a matrix form, the augmented matrix [A|b] is as shown below:
sane as above
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Tracing of Square matrices: The trace of a square matrix is the addition of all the elements on the diagonal. For illustration, for the preceding matrix it is 1 + 6 + 11 + 16,
Replacement : Replace a row by adding it to (or subtract from it) a multiple of the other row. For a given row ri, this is written as ri - srj → ri Note that when r
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