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The reduced row echelon form (RREF) of the given matrix \( A \) is:

\[
\text{RREF}(A) = \begin{pmatrix}
1 & 0 & 5.75 & 0.25 \\
0 & 1 & 0.25 & 1.75 \\
0 & 0 & 0 & 0
\end{pmatrix}
\]

This matrix is now in its fully simplified form, meaning all leading coefficients are 1, and all rows of zeroes (if any) are at the bottom.

Do you need further details or explanations? Here are some related questions you might want to explore:

1. What is the significance of a matrix being in RREF?
2. How do we interpret the pivot columns in an RREF matrix?
3. Can we solve a system of equations from this RREF form?
4. What methods exist for manually computing the RREF?
5. How does Gaussian elimination relate to finding RREF?

**Tip:** When converting a matrix to RREF, the goal is to simplify the system of equations represented by the matrix, making it easier to analyze solutions.

Encontrar la forma reducida RREF de la matriz A = [[1, 5, 7, 9], [0, 4, 1, 7], [2, -2, 11, -3]]

Este problema muestra cómo encontrar la forma reducida escalonada por filas (RREF) de una matriz dada A = [[1, 5, 7, 9], [0, 4, 1, 7], [2, -2, 11, -3]]. La solución cubre conceptos claves del álgebra lineal, como la eliminación de Gauss y las operaciones elementales sobre filas. Ideal para estudiantes de cursos avanzados de Álgebra Lineal.

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