College Algebra, Chapter 7, Review Exercises, Section Review Exercises, Problem 2

Given the matrix $\left[ \begin{array}{ccc}
1 & 0 & 6 \\
0 & 1 & 0
\end{array} \right]$.

a.) State the dimension of the matrix.


$
\begin{equation}
\begin{aligned}

& \text{Matrix} && \text{Dimension} &&&
\\
\\
& \left[ \begin{array}{ccc}
1 & 0 & 6 \\
0 & 1 & 0
\end{array} \right]
&& 2 \times 3
&&& \text{2 rows by 3 columns}

\end{aligned}
\end{equation}
$


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

Yes, the matrix is in row-echelon form.

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

Yes, the matrix is 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{equation}
\begin{aligned}

x =& 6
\\
y =& 0

\end{aligned}
\end{equation}
\right.
$