Stitz-Zeager_College_Algebra_e-book

Stitz-Zeager_College_Algebra_e-book

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Unformatted text preview: → −−−−−−−− Gauss Jordan Elimination I2 x1 x3 A 0 1 −− − − − − − −→ −−−−−−−− Gauss Jordan Elimination I2 x2 x4 Since the row operations for both processes are the same, all of the arithmetic on the left hand side of the vertical bar is identical in both problems. The only difference between the two processes is what happens to the constants to the right of the vertical bar. As long as we keep these separated into columns, we can combine our efforts into one ‘super-sized’ augmented matrix and describe the above process as A 1 0 0 1 Gauss Jordan Elimination −− − − − − − −→ −−−−−−−− I2 x1 x3 x2 x4 We have the identity matrix I2 appearing as the right hand side of the first super-sized augmented matrix and the left hand side of the second super-sized augmented matrix. To our surprise and delight, the elements on the right hand side of the second super-sized augmented matrix are none other than those which comprise A−1 . Hence, we have A I2 Gauss Jordan Elimination −− − − − − − ...
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This note was uploaded on 05/03/2013 for the course MATH Algebra taught by Professor Wong during the Fall '13 term at Chicago Academy High School.

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