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To find the rank of matrix \( A \), we will reduce it to row echelon form (or reduced row echelon form) using elementary row operations. The matrix is:

\[
A = \begin{pmatrix}
1 & 1 & -1 & -1 \\
2 & 3 & 1 & -2 \\
3 & 4 & 0 & -3
\end{pmatrix}
\]

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Would you like to walk through the steps of finding the rank manually? I can guide you through the process step by step if you'd like. 

Here are some questions to further explore this topic:

1. Do you know how to perform Gaussian elimination on a matrix?
2. Would you like to explore different methods for finding the rank of a matrix?
3. What is the importance of the rank of a matrix in linear algebra?
4. Have you ever worked with the concept of the nullity of a matrix?
5. Are you familiar with how row and column spaces relate to the rank of a matrix?

**Tip:** The rank of a matrix gives the maximum number of linearly independent rows or columns within it, which provides insight into the matrix's properties and solutions to systems of equations.

This tutorial explores how to find the rank of the matrix A using row reduction and Gaussian elimination. The matrix is A = [[1, 1, -1, -1], [2, 3, 1, -2], [3, 4, 0, -3]]. This problem covers important concepts such as matrix rank, row echelon form, and the Rank-Nullity Theorem.

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