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The rank of the given matrix, after applying the Echelon form method, is **3**.

Would you like to go over the steps for obtaining this result or have any further questions?

Here are 5 related questions you might find useful:
1. What are the steps to row-reduce a matrix to its echelon form?
2. How does echelon form differ from reduced row echelon form?
3. Can a matrix with more columns than rows still have full rank?
4. How can the rank of a matrix help in solving systems of linear equations?
5. What is the significance of pivot positions in determining the rank?

**Tip:** The rank of a matrix is the number of linearly independent rows or columns, which corresponds to the number of pivot positions in echelon form.

Apply Echelon form method to find the rank of the matrix [[2, -4, 3, -1, 0], [1, -2, -1, -4, 2], [0, 1, 3, 5, 1], [4, -7, 4, -4, 5]].

Discover how to calculate the rank of a matrix using the Echelon form method. This guide provides a step-by-step solution for the matrix [[2, -4, 3, -1, 0], [1, -2, -1, -4, 2], [0, 1, 3, 5, 1], [4, -7, 4, -4, 5]], explaining key linear algebra concepts like row reduction, pivot positions, and rank determination. Suitable for advanced high school or college-level students.

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