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My textbook gives the following system, \begin{matrix} 4- x_2 -x_3+x_4 =0 \\ x_1 +x_2+x_3+x_4 = 6\\ 2x_1 +4x_2+x_3-2x_4 = -1\\ 3x_1 +x_2-2x_3+2x_4 = 3 \end{matrix}

and supplies the answer as $$(2,-1,3,2)$$They set up the augmented matrix as follows,

$$\left[\begin{array}{rrrr|r} 0 & -1 &-1&1& 0 \\ 1 & 1 & 1&1&6\\ 2 & 4 &1&-2&-1\\ 3 & 1 &-2&2&3 \end{array}\right]$$ The solution checks out for all the equations except the first one. Why is this correct ?

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    $\begingroup$ That's not correct. Typo? $\endgroup$ – TokenToucan Feb 28 '15 at 20:38
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    $\begingroup$ the (1, 1) element differs. $\endgroup$ – marty cohen Feb 28 '15 at 20:39
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    $\begingroup$ It appears the initial $4$ should be a zero. $\endgroup$ – AMPerrine Feb 28 '15 at 20:39
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    $\begingroup$ The augmented matrix and solution are already correct. Only the first equation had a mistake. $\endgroup$ – AMPerrine Feb 28 '15 at 20:51
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    $\begingroup$ @AMPerrine Please consider converting your comment into an answer, so that this question gets removed from the unanswered tab. If you do so, it is helpful to post it to this chat room to make people aware of it (and attract some upvotes). For further reading upon the issue of too many unanswered questions, see here, here or here. $\endgroup$ – Julian Kuelshammer Apr 12 '15 at 21:15
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There is an error in the first equation of the system. If the four is replaced with a zero then both the augmented matrix and solution will be correct.

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