lecture7 - Math 006(Lecture 7 Gauss-Jordan Elimination Gauss-Jordan elimination is a process to obtain the solution for a system of linear equations

# lecture7 - Math 006(Lecture 7 Gauss-Jordan Elimination...

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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