College Algebra, Chapter 7, Review Exercises, Section Review Exercises, Problem 6

Given the matrix $\left[ \begin{array}{cccc}
1 & 8 & 6 & -4 \\
0 & 1 & -3 & 5 \\
0 & 0 & 2 & -7 \\
1 & 1 & 1 & 0
\end{array} \right]$.

a.) State the dimension of the matrix.


$
\begin{equation}
\begin{aligned}

& \text{Matrix} && \text{Dimension} &&&
\\
\\
& \left[ \begin{array}{cccc}
1 & 8 & 6 & -4 \\
0 & 1 & -3 & 5 \\
0 & 0 & 2 & -7 \\
1 & 1 & 1 & 0
\end{array}
\right]
&& 4 \times 4
&&& \text{4 rows by 4 columns}

\end{aligned}
\end{equation}
$


b.) Is the matrix in row-echelon form?

No, the matrix is not in row-echelon form.

c.) Is the matrix in reduced row-echelon form?

Not, the matrix is not in reduced row-echelon form.

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

The equivalent system of equations of the augmented matrix is


$
\left\{
\begin{array}{ccccc}
x & +8y & +6z & = & -4 \\
& y & -3z & = & 5 \\
x & +y & +z & = & 0
\end{array}
\right.
$