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