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The rank of the given matrix is \(4\).

Would you like more details or have any questions about how the rank was determined?

Here are some related questions you might explore:
1. What is the significance of matrix rank in linear algebra?
2. How can we use row-reduction to calculate the rank of a matrix?
3. What does a full-rank matrix indicate in terms of linear independence?
4. How do you find the nullity of a matrix given its rank?
5. Can the rank of a matrix change if a row or column is added?

**Tip:** The rank of a matrix represents the maximum number of linearly independent rows or columns.

Find the rank of the matrix: 
[ [1, -1, 2, -2], 
  [4, 1, 0, 2], 
  [0, 3, 1, 4], 
  [0, 1, 0, 2] ]

This page explains how to determine the rank of the matrix [ [1, -1, 2, -2], [4, 1, 0, 2], [0, 3, 1, 4], [0, 1, 0, 2] ] through Gaussian elimination and row reduction techniques. Learn about the concepts of linear independence and the Rank-Nullity Theorem.

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