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The given system of equations has been reduced to Row-Reduced Echelon Form (RREF). The final matrix is:

\[
\begin{pmatrix}
1 & 3 & 0 & 3 & 0 \\
0 & 0 & 1 & -1 & 0 \\
0 & 0 & 0 & 0 & 1
\end{pmatrix}
\]

This corresponds to the following system of equations:
1. \( w + 3x + 3z = 0 \)
2. \( y - z = 0 \)
3. \( 0 = 1 \)

However, the third row indicates that this system is inconsistent because \( 0 \neq 1 \), meaning there is no solution to the system.

Would you like further clarification or a detailed breakdown of the row operations?

Here are 5 related questions for practice:
1. How do you interpret an inconsistent system in RREF?
2. What is the difference between REF and RREF?
3. Can an inconsistent system still have infinitely many solutions?
4. How does Gaussian elimination differ from Gauss-Jordan elimination?
5. How do you check if a matrix is in RREF?

**Tip:** Inconsistent systems can occur when row reduction leads to a contradiction like \(0 = 1\), meaning no solution exists.

Put the following system in RREF. Show your row operations: w + 3x + y + 2z = -1, w + 3x + 3y = 3, -2w - 6x + y - 7z = 8.

This problem involves reducing a system of linear equations to Row-Reduced Echelon Form (RREF) using Gaussian elimination and row operations. It tests knowledge in Linear Algebra, including solving systems of equations and recognizing inconsistencies.

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