Answer
a.$\quad$ the matrix is not in row-echelon form.
b.$\quad$the matrix is not in reduced row-echelon form.
c.$\quad\left\{\begin{array}{rrrr}
x & & & =0\\
& & 0 & =0\\
& y & +5z & =1
\end{array}\right.$
Work Step by Step
A matrix is in row-echelon form if it satisfies the following conditions.
1. The first nonzero number in each row (reading from left to right) is 1. This is called the leading entry.
2. The leading entry in each row is to the right of the leading entry in the row immediately above it.
3. All rows consisting entirely of zeros are at the bottom of the matrix.
A matrix is in reduced row-echelon form if it is in row-echelon form and alsosatisfies the following condition.
4. Every number above and below each leading entry is a 0.
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a.
(3) is not satisfied, the matrix is not in row-echelon form.
b.
Since it's not in row-echelon form,
the matrix is not in reduced row-echelon form.
c.
The augmented matrix has rows representing each equation.
Each row contains the coefficients of the variables on the LHS, followed by the constant of the RHS:
$\left\{\begin{array}{rrrr}
x & & & =0\\
& & 0 & =0\\
& y & +5z & =1
\end{array}\right.$