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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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    $\begingroup$ the (1, 1) element differs. $\endgroup$ Commented Feb 28, 2015 at 20:39
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    $\begingroup$ It appears the initial $4$ should be a zero. $\endgroup$ Commented Feb 28, 2015 at 20:39
  • $\begingroup$ Yeah just found the errata for the textbook. The 4 was suppose to be a 0. If the 4 were suppose to be there, how would you set up the augmented matrix ? $\endgroup$ Commented Feb 28, 2015 at 20:44
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    $\begingroup$ The augmented matrix and solution are already correct. Only the first equation had a mistake. $\endgroup$ Commented Feb 28, 2015 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. $\endgroup$ Commented Apr 12, 2015 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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