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

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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 0 0 2 3 4 0 2 3 - 4 1 0 - 2 - 1 7 3 r 2 r 3 -----→ 1 1 - 5 2 1 2 0 2 3 - 4 1 0 0 2 3 4 0 - 2 - 1 7 3 1 2 r 2 r 2 ------→ 1 1 - 5 2 1 2 0 1 3 2 - 2 1 2 0 0 2 3 4 0 - 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 0 , H 1
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3 Determinant Only for square matrix, we take a sub matrix of the matrix A , which is, A 1 = 0 2 3 0 0 2 2 2 - 5 Gauss Elimination -----------→ H 1 = 1 1 - 5 2 0 1 3 2 0 0 1
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