Handout-better7 - Examples Examples Gauss-Jordan Elimination MATH 1003 Calculus and Linear Algebra(Lecture 7 Maosheng Xiong Department of Mathematics

Handout-better7 - Examples Examples Gauss-Jordan...

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Examples MATH 1003 Calculus and Linear Algebra (Lecture 7) Maosheng Xiong Department of Mathematics, HKUST Maosheng Xiong Department of Mathematics, HKUST MATH 1003 Calculus and Linear Algebra (Lecture 7) Examples Gauss-Jordan Elimination In the last lecture, we learned how to solve a system of 2 equations with 2 variables by performing row operations on its augmented matrix. Now, we generalize this method so that it can be applied to any system of linear equations. It is called the Gauss-Jordan elimination . The idea is very simple: We transform the corresponding augmented matrix by row operations to a simple form. And the solution(s) to the linear system corresponding to this simple form (which is(are) also the solution(s) to the original system) can be obtained easily. Maosheng Xiong Department of Mathematics, HKUST MATH 1003 Calculus and Linear Algebra (Lecture 7) Examples Reduced Form Definition 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.

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