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I'm trying to figure out how my professor got to the step circled in red in the image below:

enter image description here

How did he get the values of the first row to become completely positive, and how did he derive the values of the entire 2nd row?

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The second entry in the first row is -1, that's probably a typo of your professor. For the second row, he did a row operation by row 2 -> row 2 - h times row 1. –  user27126 Feb 26 '13 at 6:24
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Perhaps has trouble with minus signs. I certainly do. –  André Nicolas Feb 26 '13 at 6:26
    
And for the other encircling: "which values" would be prefered? –  Hagen von Eitzen Feb 26 '13 at 7:46

2 Answers 2

up vote 12 down vote accepted

its very easy..... he just multiplied the first row with the negative of "h" and added it to the second row. although some misprinting is there in the last matrix where in second column, first entry should be -1.

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The entry in the first row and second column was misprinted as $1$ when it should be $-1$. The change to the second row is a standard row operation, replacing row 2 with row 2 minus $h$ times row 1.

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