jerri-1-2 - Section 1.2 Gauss-Jordan Elimination There are...

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Section 1.2 Gauss-Jordan Elimination There are three legal elementary row operations : (1) Multiply a row by a nonzero constant. Example: 1 2 R would multiply every entry in the first row of a matrix by 2. (2) Switch two rows. Example: 12 R R would interchange the elements in the first and second rows. (3) Add a multiple of one row to another. Example: 2 R R + would add twice the elements in the second row to the elements in the first row. Note that whatever is written first is what changes.
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Gauss-Jordan Elimination is made up of any combination of these row operations. Our goal is to get 10 01 a b    or 100 010 001 x y z Example: Use Gauss-Jordan Elimination to solve 12 25 34 5 xx += −= Note: This is a 2X2 system. Solution: First form the augmented matrix. 5 5 −− Now use the elementary row operations to make it look like r s
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21 3 R R 2 1 : 345 3:361 5 01 0 2 0 R R −− −−− 12 5 0 2 0    2 1 10 R 5 2 2 RR 1 2 : 5 2:024 10 1 R R 1 2 x 1 = 1 & x 2 = 2
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This note was uploaded on 07/16/2008 for the course MATH 1114 taught by Professor Jhengland during the Fall '08 term at Virginia Tech.

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jerri-1-2 - Section 1.2 Gauss-Jordan Elimination There are...

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