College Algebra, Chapter 7, 7.1, Section 7.1, Problem 18

A matrix is $\left[ \begin{array}{cccccc}
1 & 3 & 0 & 1 & 0 & 0 \\
0 & 1 & 0 & 4 & 0 & 0 \\
0 & 0 & 0 & 1 & 1 & 2 \\
0 & 0 & 0 & 1 & 0 & 0
\end{array} \right]$.

a.) Determine whether the matrix is in row-echelon form.

The given matrix is not a row-echelon form.

b.) Determine whether the matrix is in reduced row-echelon form.

The given matrix is a reduced row-echelon form.

c.) Write the system of equations for which the given matrix is the augmented matrix.


$
\left\{
\begin{array}{cccccc}
x & + 3y & + w & & = & 0 \\
& y & + 4w & & = & 0 \\
& & w & +d & = & 2 \\
& & w & & = & 0
\end{array}

\right.
$