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lecture7hout - MATH 006 Calculus and Linear Algebra...

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Unformatted text preview: MATH 006 Calculus and Linear Algebra (Lecture 7) Albert Ku HKUST Mathematics Department Albert Ku (HKUST) MATH 006 1 / 15 Outline 1 Gauss-Jordan Elimination 2 Examples Albert Ku (HKUST) MATH 006 2 / 15 Gauss-Jordan Elimination 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. Albert Ku (HKUST) MATH 006 3 / 15 Gauss-Jordan Elimination 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....
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This note was uploaded on 12/28/2010 for the course MATH MATH006 taught by Professor Forgot during the Fall '09 term at HKUST.

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lecture7hout - MATH 006 Calculus and Linear Algebra...

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