## If the Augmented Matrix is Row-Equivalent to the Identity Matrix, is the System Consistent?

## Problem 695

Consider the following system of linear equations:

\begin{align*}

ax_1+bx_2 &=c\\

dx_1+ex_2 &=f\\

gx_1+hx_2 &=i.

\end{align*}

**(a)** Write down the augmented matrix.

**(b)** Suppose that the augmented matrix is row equivalent to the identity matrix. Is the system consistent? Justify your answer.