Simple Gauss-Jordan Elimination

[Saladsamurai]

I have done the following problem over and over and keep getting the same result. So either the book answer is wrong or I am making the same mistake over again:

\left[\begin{array} {cccc}<br /> 5&amp;-2&amp;6&amp;0\\<br /> -2&amp;1&amp;3&amp;1\\<br /> \end{array}\right]

\left[\begin{array} {cccc}<br /> 1&amp;-\frac25&amp;\frac65&amp;0\\<br /> -2&amp;1&amp;3&amp;1\\<br /> \end{array}\right]

\left[\begin{array} {cccc}<br /> 1&amp;-\frac25&amp;\frac65&amp;0\\<br /> 0&amp;\frac15&amp;\frac{17}{5}&amp;1\\<br /> \end{array}\right]

\left[\begin{array} {cccc}<br /> 1&amp;0&amp;8&amp;2\\<br /> 0&amp;1&amp;17&amp;5\\<br /> \end{array}\right]

Am I screwing this up somewhere?

 

[Mark44]

I have done the following problem over and over and keep getting the same result. So either the book answer is wrong or I am making the same mistake over again:

\left[\begin{array} {cccc}<br /> 5&amp;-2&amp;6&amp;0\\<br /> -2&amp;1&amp;3&amp;1\\<br /> \end{array}\right]

\left[\begin{array} {cccc}<br /> 1&amp;-\frac25&amp;\frac65&amp;0\\<br /> -2&amp;1&amp;3&amp;1\\<br /> \end{array}\right]

\left[\begin{array} {cccc}<br /> 1&amp;-\frac25&amp;\frac65&amp;0\\<br /> 0&amp;\frac15&amp;\frac{17}{5}&amp;1\\<br /> \end{array}\right]

\left[\begin{array} {cccc}<br /> 1&amp;0&amp;8&amp;2\\<br /> 0&amp;1&amp;17&amp;5\\<br /> \end{array}\right]

Am I screwing this up somewhere?

I ended up with different numbers in the 3rd column.
\left[\begin{array} {cccc}<br /> 1&amp;0&amp;12&amp;2\\<br /> 0&amp;1&amp;27&amp;5\\<br /> \end{array}\right]

In my first step, I added 2 times row 1 to -5 times row 2. Then I added 2 times row 2 to row 1. Finally, I replaced row 1 with 1/5 of itself. It is usually simpler to keep integer values for as long as possible.

 

[aPhilosopher]

@Saladsamurai, [STRIKE]When you go to eliminate the -2, you want to add row 1 to row 2. You're subtracting it.[/STRIKE]

3 + 12/5 = 15/5 + 12/5 = 27/5

 

[Saladsamurai]

Yeah! I just caught that :/ Man.. I must have added 6/5+3=17/5
like ten times! Stupid brain gets sucked into following
a pattern

thanks!