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The reduced row echelon form (RREF) of the given matrix

\[
\begin{pmatrix}
1 & 1 & 3 \\
3 & 5 & 8 \\
2 & -1 & 3
\end{pmatrix}
\]

is:

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

This is the identity matrix, indicating that the original matrix is invertible and has full rank.

Would you like to go over any specific steps or need further explanation? Here are 5 related questions to explore:

1. How do you determine if a matrix is invertible using row reduction?
2. What is the significance of reduced row echelon form in solving linear systems?
3. How can RREF be used to find the rank of a matrix?
4. What are the properties of a matrix that lead to a diagonal RREF?
5. How do you interpret free variables when solving a system using RREF?

**Tip:** The RREF is particularly useful for solving systems of linear equations, as it simplifies the matrix to a form where solutions can be easily read off.

Reduce the following matrix to its row reduced echelon form:
\begin{pmatrix}
1 & 1 & 3 \\
3 & 5 & 8 \\
2 & -1 & 3
\end{pmatrix}

This example demonstrates how to reduce a matrix to its row reduced echelon form (RREF) using row reduction techniques. The matrix \begin{pmatrix}1 & 1 & 3 \\ 3 & 5 & 8 \\ 2 & -1 & 3\end{pmatrix is reduced to the identity matrix, indicating that it is invertible with full rank. Learn about matrix operations, Gaussian elimination, and key theorems such as the Invertible Matrix Theorem.

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