Determine which of the following systems of equations is in row-echelon form. System I: $\left\{ \begin{aligned}
x - 8 y + 6 z & = 2 \
y - 7 z & = - 19 \
z & = 17
\end{aligned} \right.$ System II: $$\left\{ \begin{aligned}
x - 6 y - 8 z & = 2 \
2 y + 5 z & = - 1 \
z & = - 3
\end{aligned} \right.$$ System III: $$\left\{ \begin{aligned}
x - 4 y - z & = 20 \
y + 3 z & = 14 \
z & = 9
\end{aligned} \right.$$
A)None of the systems are in row-echelon form.
B)Only system I is in row-echelon form.
C)Only systems I and III are in row-echelon form.
D)Only systems I and II are in row-echelon form.
E)Only systems II and III are in row-echelon form.

Question

Quizplus · Accepted Answer

System I and System III are in row-echelon form because each leading coefficient (the first non-zero number from the left, in each row) is to the right of the leading coefficient of the row above it, and all entries below a leading coefficient are zero.

Determine Which of the Following Systems of Equations Is in Row-Echelon