https://file.aiquickdraw.com/mathbot/file/1730187772963jwwxpn09.jpg

To continue the row reduction process, let’s examine the current matrix after the transformations you've already performed:

\[
\begin{pmatrix}
2 & 1 & -2 & | & 10 \\
-3 & -1 & 8 & | & -20 \\
12 & 14 & 33 & | & -59 \\
\end{pmatrix}
\]

### Step-by-Step Continuation

1. **Goal**: Transform the leading entry in the third row (12) to 1 by dividing the entire row by 12.
   \[
   R_3 \rightarrow \frac{1}{12} R_3
   \]
   Resulting in:
   \[
   \begin{pmatrix}
   2 & 1 & -2 & | & 10 \\
   -3 & -1 & 8 & | & -20 \\
   1 & \frac{7}{6} & \frac{11}{4} & | & -\frac{59}{12} \\
   \end{pmatrix}
   \]

2. **Eliminate** the first entry in the third row (1 under the 2 in the first row) by applying:
   \[
   R_1 \rightarrow R_1 - 2 \times R_3
   \]
   After performing the operation, the first row becomes:
   \[
   \begin{pmatrix}
   0 & -\frac{5}{3} & -\frac{29}{6} & | & \frac{89}{6} \\
   -3 & -1 & 8 & | & -20 \\
   1 & \frac{7}{6} & \frac{11}{4} & | & -\frac{59}{12} \\
   \end{pmatrix}
   \]

3. **Eliminate** the first entry in the second row by adding 3 times the third row to the second row:
   \[
   R_2 \rightarrow R_2 + 3 \times R_3
   \]

Perform this to achieve further row simplifications. Let me know if you want details on this or have specific questions. 

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### Follow-Up Questions
1. Would you like a detailed breakdown of each arithmetic step?
2. Should I explain how to convert this into a Reduced Row Echelon Form (RREF)?
3. Are you interested in learning how these transformations relate to finding the solution set?
4. Do you need assistance with interpreting the result of this matrix operation?
5. Do you want help verifying each step for accuracy?

### Tip
Always double-check each row operation as small errors can propagate through each step and affect the final result.

Explore how to continue the matrix row reduction process using Gaussian elimination. This step-by-step solution covers key concepts in matrix operations, including elementary row operations and transformation into row echelon form. Suitable for high school students in Grades 10-12.

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