lecture7 - the row operation required to transform the...

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Math 006 (Lecture 7) Gauss-Jordan Elimination Gauss-Jordan elimination is a process to obtain the solution for a system of linear equations. Target of Gauss-Jordan elimination: We would like to reduce an augmented matrix to its reduced form . Definition 1. A matrix is said to be in reduced form if it satisfies 1. Each row consisting entirely of zeros is below any row having at least one nonzero element. 2. The leftmost nonzero element in each row is 1. 3. All other elements in the column containing the leftmost 1 of a given row are zeros. 4. The leftmost 1 in any row is to the right of the leftmost 1 in the row above. Procedure of Gauss-Jordan elimination: Apply a sequence of row operations on the augmented matrix. Example 1. Indicate which condition in the definition is violated for each matrix. State
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Unformatted text preview: the row operation required to transform the matrix into reduced form. (a) ± 0 1 ² ²-2 1 0 ² ² 3 ³ (b) ± 1 2-2 ² ² 3 0 0 1 ² ²-1 ³ (c)     1 0 ² ²-3 0 0 ² ² 0 1 ² ²-2 0 1 ² ²-2     (d)   1 0 0 ² ²-1 0 2 0 ² ² 3 0 0 1 ² ²-5   1 Application of Gauss-Jordan elimination: Solving system of linear equations. Example 2. Solve      3 x 1 + 8 x 2-x 3 =-18 2 x 1 + x 2 + 5 x 3 = 8 2 x 1 + 4 x 2 + 2 x 3 =-4 Example 3. Solve ± 2 x 1-x 2-3 x 3 = 8 x 1-2 x 2 = 7 Example 4. Solve      4 x 1-x 2 + 2 x 3 = 3-4 x 1 + x 2-3 x 3 =-10 8 x 1-2 x 2 + 9 x 3 =-1 2...
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This note was uploaded on 09/04/2010 for the course MATH MATH006 taught by Professor Forgot during the Fall '09 term at HKUST.

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lecture7 - the row operation required to transform the...

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