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The rank of the given matrix is 3.

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Here are five related questions for further practice:
1. What is the definition of the rank of a matrix?
2. How can we find the rank of a matrix using Gaussian elimination?
3. What does the rank of a matrix tell us about its row or column independence?
4. Can a matrix have a rank higher than its smallest dimension (number of rows or columns)?
5. How does the determinant of a matrix relate to its rank?

**Tip:** The rank of a matrix is the maximum number of linearly independent rows or columns, which means it provides insight into the dimension of the space spanned by the matrix.

Find the rank of the matrix [ [1, -1, 0, 2, 1], [3, 1, 1, -1, 2], [4, 0, 1, 0, 3], [9, -1, 2, 3, 7] ]

This problem involves finding the rank of a 4x5 matrix using Gaussian elimination and row reduction techniques. Learn step-by-step how to reduce the matrix to its row echelon form and determine the number of linearly independent rows, which gives the rank.

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