| 1. | The second column describes which row operations have just been performed.
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| 2. | However, these whole-row operations are generally rare.
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| 3. | These transformations are the analogues of the elementary row operations.
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| 4. | However, such whole-row operations are generally rare.
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| 5. | These row operations are labelled in the table as
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| 6. | Then we perform row operations on the matrix.
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| 7. | One can think of each row operation as the left product by an elementary matrix.
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| 8. | Elementary row operations are used in Gaussian elimination to reduce a matrix to row echelon form.
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| 9. | The elementary matrix for any row operation is obtained by executing the operation on the identity matrix.
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| 10. | This final form is unique; in other words, it is independent of the sequence of row operations used.
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