An augmented matrix that represents a system of linear equations (in variables $x , y$, and $z$ ) has been reduced using Gauss-Jordan elimination. Write the solution represented by the augmented matrix.
$$\left[ \begin{array} { c c c : c }
1 & 0 & 0 & - 1 \
0 & 1 & 0 & 3 \
0 & 0 & 1 & 8
\end{array} \right]$$
A) $x = - 1 , y = 3 , z = 8$
B) $x = 1 , y = - 3 , z = - 8$
C) $x = 0 , y = 0 , z = 0$
D) $x = - x , y = 8 y , z = 3 z$
E) $\quad x = - 1 , y = 0 , z = 0$

Question

An augmented matrix that represents a system of linear equations (in variables $x , y$, and $z$ ) has been reduced using Gauss-Jordan elimination. Write the solution represented by the augmented matrix.
$$\left[ \begin{array} { c c c : c } 
1 & 0 & 0 & - 1 \
0 & 1 & 0 & 3 \
0 & 0 & 1 & 8
\end{array} \right]$$
A) $x = - 1 , y = 3 , z = 8$
B) $x = 1 , y = - 3 , z = - 8$
C) $x = 0 , y = 0 , z = 0$
D) $x = - x , y = 8 y , z = 3 z$
E) $\quad x = - 1 , y = 0 , z = 0$

Quizplus · Accepted Answer

The augmented matrix is in reduced row echelon form, directly showing the solutions for $x, y,$ and $z$ as $x = -1, y = 3,$ and $z = 8$, respectively.

An Augmented Matrix That Represents a System of Linear Equations x,yx , yx,y

An Augmented Matrix That Represents a System of Linear Equations $x , y$