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}

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}

Question
Forms of linear equations
asked 2021-02-25
Form (a) the coefficient matrix and (b) the augmented matrix for the system of linear equations \(\begin{cases}9x-3y+z=13 \\ 12x-8z=5 \\ 3x+4y-z =6 \end{cases}\)

Answers (1)

2021-02-26
For a system of equations \(\begin{cases}ax+by+cz=j \\ dx+ey+fz=k \\ gx+hy+iz =l \end{cases}\)
, the coefficient matrix is \(\begin{bmatrix} a&b&c \\ d&e&f\\ g&h&i \end{bmatrix}\) and the augmented matrix is \(\begin{bmatrix}a&b&c&j\\ d&e&f&k\\ g&h&i&l \end{bmatrix}\)
a) For the system \(\begin{cases}9x-3y+z=13 \\ 12x-8z=5 \\ 3x+4y-z =6 \end{cases} a=9 ,b=-3,c=1,d=12,e=0,f=-8,g=3,h=4 and i=-1\) so the coefficient matrix is \(\begin{bmatrix}9&-3&1\\ 12&0&-8\\ 3&4&-1 \end{bmatrix}\)
b) For the system \(\begin{cases}9x-3y+z=13 \\ 12x-8z=5 \\ 3x+4y-z =6 \end{cases} a=9 ,b=-3,c=1,d=12,e=0,f=-8,g=3,h=4 , i=-1 , j=13, k=5 and l=6\) so the coefficient matrix is \(\begin{bmatrix}9&-3&1\\ 12&0&-8\\ 3&4&-1 \end{bmatrix}\) so the augmented matrix is \(\begin{bmatrix}9&-3&1&13\\ 12&0&-8&5\\ 3&4&-1&6 \end{bmatrix}\)
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