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


$\left\{ \begin{equation} \begin{aligned} x =& 6 \\ y =& 0 \end{aligned} \end{equation} \right.$