# Form (a) the coefficient matrix and (b) the augmented matrix for the system of linear equations. displaystyle{leftlbracebegin{matrix}{x}+{y}={0}{5}{x}-{2}{y}-{2}{z}={12}{2}{x}+{4}{y}+{z}={5}end{matrix}right.}

Form (a) the coefficient matrix and (b) the augmented matrix for the system of linear equations.
$\left\{\begin{array}{c}x+y=0\\ 5x-2y-2z=12\\ 2x+4y+z=5\end{array}$
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Cristiano Sears
For a system of equations $\left\{\begin{array}{c}ax+by+cz=j\\ dx+ey+fz=k\\ gx+hy+iz=l\end{array}$
, the coefficient matrix is $\left[\begin{array}{ccc}a& b& c\\ d& e& f\\ g& h& i\end{array}\right]$ and the augmented matrix is $\left[\begin{array}{ccccc}a& b& c& |& j\\ d& e& f& |& k\\ g& h& i& |& l\end{array}\right]$
a) For the system $\left\{\begin{array}{c}x+y=0\\ 5x-2y-2z=12\\ 2x+4y+z=5\end{array}$
a=1 , b=1 , c=0,d=5,e=-2, f=-2, g=2 , h=4 and i=1 so the coefficient matrix is $\left[\begin{array}{ccc}5& 1& 0\\ 5& -2& -2\\ 2& 4& 1\end{array}\right]$
b) For the system $\left\{\begin{array}{c}x+y=0\\ 5x-2y-2z=12\\ 2x+4y+z=5\end{array}$
a=1 , b=1 , c=0,d=5,e=-2, f=-2, g=2 , h=4 , i=1 , j=0 , k=12 and l=5 so the augmented matrix is $\left[\begin{array}{ccccc}5& 1& 0& |& 0\\ 5& -2& -2& |& 12\\ 2& 4& 1& |& 5\end{array}\right]$
a) $\left[\begin{array}{ccc}5& 1& 0\\ 5& -2& -2\\ 2& 4& 1\end{array}\right]$
b) $\left[\begin{array}{ccccc}5& 1& 0& |& 0\\ 5& -2& -2& |& 12\\ 2& 4& 1& |& 5\end{array}\right]$
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