T7 - ERG2018 Tutorial Notes 7 1 Three Type Elementary Row...

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Unformatted text preview: ERG2018 Tutorial Notes 7 1 Three Type Elementary Row Operations 1. Type I : Interchange any two rows i and j . r i ↔ r j . 2. Type II : Multiply row i by a nonzero number k . k r i → r i . 3. Type III : Add a multiple k of row i to another j . k r i + r j → r j . 2 Gauss Elimination A =     0 2 3- 4 1 0 0 2 3 4 2 2- 5 2 4 2 0- 6 9 7     r 1 ↔ r 3-----→     2 2- 5 2 4 0 0 2 3 4 0 2 3- 4 1 2 0- 6 9 7     1 2 r 1 → r 1------→     1 1- 5 2 1 2 0 0 2 3 4 0 2 3- 4 1 2 0- 6 9 7    - 2 r 1 + r 4 → r 4----------→     1 1- 5 2 1 2 2 3 4 2 3- 4 1- 2- 1 7 3     r 2 ↔ r 3-----→     1 1- 5 2 1 2 2 3- 4 1 2 3 4- 2- 1 7 3     1 2 r 2 → r 2------→     1 1- 5 2 1 2 1 3 2- 2 1 2 2 3 4- 2- 1 7 3     2 r 2 + r 4 ↔ r 4--------→     1 1- 5 2 1 2 0 1 3 2- 2 1 2 0 0 2 3 4 0 0 2 3 4     1 2 r 3 → r 3------→     1 1- 5 2 1 2 0 1 3 2- 2 1 2 0 0 1 3 2 2 0 0 2 3 4    - 2 r 3 + r 4 ↔ r 4----------→     1 1- 5 2 1 2 0 1 3 2- 2 1 2 0 0 1 3 2 2 0 0 0 0     , H 1 3 Determinant Only for square matrix, we take a sub matrix of the matrix...
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This note was uploaded on 11/13/2010 for the course SEEM SEEM2018 taught by Professor Chan during the Spring '10 term at CUHK.

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T7 - ERG2018 Tutorial Notes 7 1 Three Type Elementary Row...

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