week8_GE - 9/27/2011 Gausseliminationmethodusing

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9/27/2011 1 Gauss elimination method using elementary row operations (EROs) Interchange any two rows r i r j Multiply any row with a non zero constant “m” r i m* r i Add or subtract multiple of a row to another row r i m*r i ±r j 1 Example of elementary row operations LAE Problem: 2x + y = 4 ‐‐‐ (1) 8x + 2y = 12 ‐‐‐‐ (2) Matrix problem Ax = b [A] = 21 82    x y [x] = 4 12 [b] = ERO 1 (r1 r2) : The above LAE can be written as: 8x + 2y = 8 2x + y = 4 [A] = x y [x] = 12 4 [b] = ERO 2 (r1 2*r1): Multiply eqn. (1) with 2: 4x + 2y = 8 8x + 2y = 12 [A] = 42 x y [x] = 8 12 [b] = Example for ERO 3 LAE Problem: 2x + y = 4 ‐‐‐ (1) 8x + 2y = 12 ‐‐‐‐ (2) Matrix problem Ax = b [A] = x y [x] = 4 12 [b] = ERO 3 [r2 (0.25*r2 r1)]: Multiply eqn. (2) with 0.25 and subtract from (1) 2x +y = 4 0.5y = 1 [A] = 0 0.5 x y [x] = 4 1 [b] = Note, ERO operations never altered the final solution.
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This note was uploaded on 11/14/2011 for the course CE 3010 taught by Professor Clement during the Fall '09 term at Auburn University.

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