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) $x = - 1 , y = 0 , z = 0$

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) $x = - 1 , y = 0 , z = 0$

Quizplus · Accepted Answer

The row reduced form of the augmented matrix represents the system of linear equations as:
$$\begin{aligned} x &= -1 \ y &= 3 \ z &= 8 \end{aligned}$$
This is the unique solution to the system, as every variable has a value assigned to it. The correct choice is therefore A.

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