https://file.aiquickdraw.com/mathbot/file/17236362498060t0yk5ay.jpg

The matrix \( A \) given in the image is:

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

After reducing this matrix to its row echelon form (or normal form), the rank of the matrix is found to be **3**.

Would you like a detailed explanation on how to reduce the matrix to its row echelon form and determine the rank, or do you have any other questions?

Here are some related questions you might find useful:
1. How is row reduction to normal form (RREF) performed?
2. What is the significance of the rank of a matrix?
3. How can the rank of a matrix be used to determine the solution of a linear system?
4. Can a matrix have a rank greater than the number of rows or columns?
5. How does the rank of a matrix relate to its determinant?
6. What is the geometric interpretation of the rank of a matrix?
7. How can the row and column space of a matrix be determined?
8. What are some practical applications of matrix rank in engineering and science?

**Tip:** When performing matrix row operations, always keep track of each step to ensure the matrix is simplified correctly, which helps avoid errors in calculating the rank.

Learn how to reduce a matrix to its row echelon form and determine its rank. Step-by-step explanation with an example matrix A = [2 1 -3; 3 -3 -1; 1 1 2]. Understand the significance of matrix rank and its application in solving linear systems.

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