Solution to the following system of linear equations?

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 ?

• That's not correct. Typo? – TokenToucan Feb 28 '15 at 20:38
• the (1, 1) element differs. – marty cohen Feb 28 '15 at 20:39
• It appears the initial $4$ should be a zero. – AMPerrine Feb 28 '15 at 20:39
• The augmented matrix and solution are already correct. Only the first equation had a mistake. – AMPerrine Feb 28 '15 at 20:51
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