# Form (a) the coefficient matrix and (b) the augmented matrix for the system of linear equations begin{cases}9x-3y+z=13 12x-8z=5 3x+4y-z =6 end{cases}

hexacordoK 2021-02-25 Answered
Form (a) the coefficient matrix and (b) the augmented matrix for the system of linear equations $\left\{\begin{array}{l}9x-3y+z=13\\ 12x-8z=5\\ 3x+4y-z=6\end{array}$
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## Expert Answer

irwchh
Answered 2021-02-26 Author has 102 answers
For a system of equations $\left\{\begin{array}{l}ax+by+cz=j\\ dx+ey+fz=k\\ gx+hy+iz=l\end{array}$
, 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 $\left[\begin{array}{cccc}a& b& c& j\\ d& e& f& k\\ g& h& i& l\end{array}\right]$
a) For the system $\left\{\begin{array}{l}9x-3y+z=13\\ 12x-8z=5\\ 3x+4y-z=6\end{array}a=9,b=-3,c=1,d=12,e=0,f=-8,g=3,h=4andi=-1$ so the coefficient matrix is $\left[\begin{array}{ccc}9& -3& 1\\ 12& 0& -8\\ 3& 4& -1\end{array}\right]$
b) For the system $\left\{\begin{array}{l}9x-3y+z=13\\ 12x-8z=5\\ 3x+4y-z=6\end{array}a=9,b=-3,c=1,d=12,e=0,f=-8,g=3,h=4,i=-1,j=13,k=5andl=6$ so the coefficient matrix is $\left[\begin{array}{ccc}9& -3& 1\\ 12& 0& -8\\ 3& 4& -1\end{array}\right]$ so the augmented matrix is $\left[\begin{array}{cccc}9& -3& 1& 13\\ 12& 0& -8& 5\\ 3& 4& -1& 6\end{array}\right]$
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