The matrices provided need to be converted into row echelon form (REF) and reduced row echelon form (RREF) using elementary row operations (EROs). Let's start by determining the REF and RREF for each matrix. Here are the matrices from the image:

1. $\begin{bmatrix} 3 & 1 & 2 \\ 8 & -9 & 1 \end{bmatrix}$
2. $\begin{bmatrix} 1 & -1 & 1 \\ 1 & 2 & -1 \\ 1 & 1 & 1 \end{bmatrix}$
3. $\begin{bmatrix} 1 & -1 & 0 & 3 \\ 2 & 2 & 1 & 5 \end{bmatrix}$

I'll begin by converting each of these matrices into REF and RREF forms. Starting with the first matrix:

Matrix 1

• Original: $\begin{bmatrix} 3 & 1 & 2 \\ 8 & -9 & 1 \end{bmatrix}$

Row Echelon Form (REF)

• Divide the first row by 3 to make the leading entry a 1.
• Subtract $\frac{8}{3}$ times the first row from the second row to make the entry below the leading 1 a 0.

Reduced Row Echelon Form (RREF)

• Continue from the REF form and make further adjustments to achieve the identity matrix where possible.

Let's calculate these forms now.