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.
$$\left[ \begin{array} { c c c : c }
1 & 0 & 0 & 9 \
0 & 1 & 0 & 8 \
0 & 0 & 1 & - 7
\end{array} \right]$$
A) $x = 9 , y = 8 , z = - 7$
B) $x = - 9 , y = - 8 , z = 7$
C) $x = 0 , y = 0 , z = 0$
D) $x = 9 x , y = - 7 y , z = 8 z$
E) $x = 9 , y = 0 , z = 0$

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.
$$\left[ \begin{array} { c c c : c } 
1 & 0 & 0 & 9 \
0 & 1 & 0 & 8 \
0 & 0 & 1 & - 7
\end{array} \right]$$
A) $x = 9 , y = 8 , z = - 7$
B) $x = - 9 , y = - 8 , z = 7$
C) $x = 0 , y = 0 , z = 0$
D) $x = 9 x , y = - 7 y , z = 8 z$
E) $x = 9 , y = 0 , z = 0$

Quizplus · Accepted Answer

In the reduced augmented matrix, the first row implies that $x = 9$, the second row implies that $y = 8$, and the third row implies that $z = -7$. Therefore, the solution is $x = 9, y = 8, z = -7$, so the best choice is A.

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