242LN2.3 - 2.3. Determinants and Elementary Row Operations...

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Unformatted text preview: 2.3. Determinants and Elementary Row Operations The bad news is: Row operations can change the determinant of the matrix. The good news is: They do it in a predictable way. Let D old be the determinant of the matrix before a row operation, and D new the determinant of the matrix after the row operation. If two rows are swapped, then D old =- D new . If one row is added to a multiple of another row, then D old = D new . If a row is multiplied by , then D old = 1 D new . (This is the one you cant get backwards!) It is easier if you keep track of the original determinant, in terms of the new determinant, as you go along. For example, find 1 4 2 4 2 1 2- 2 14 . 1 4 2 4 2 1 2- 2 14 1 4 2 4 2 1 2- 2 14 ======= 2- 4 1 1 4 2- 14- 7 2- 2 14 1 4 2 4 2 1 2- 2 14 ======= 2- 4 1 1 4 2- 14- 7 2- 2 14 ======= 3- 2 1 1 4 2- 14- 7- 10 10 1 4 2 4 2 1 2- 2 14 ======= 2- 4 1 1 4 2- 14- 7 2- 2 14 ======= 3- 2 1 1 4 2- 14- 7- 10 10 ======= 2 3 (- 1) 1 4 2- 10 10- 14- 7 1 4 2 4 2 1 2...
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242LN2.3 - 2.3. Determinants and Elementary Row Operations...

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