To determine the rank of a matrix \(A\), we need to find the maximum number of linearly independent rows or columns in the matrix. The rank of a matrix is also equal to the number of non-zero rows in its row echelon form or reduced row echelon form (RREF).

However, you haven't provided the specific matrix \(A\) for which you want to determine the rank. If you provide the matrix, I can compute the rank for you. 

If you want to compute the rank of a matrix, here's a general outline of the steps:

1. **Convert the matrix to row echelon form (REF)** or **reduced row echelon form (RREF)**.
2. **Count the number of non-zero rows** in the echelon form. This count is the rank of the matrix.

Please provide the matrix \(A\), and I will calculate its rank.

Would you like more details on how to compute the REF or RREF of a matrix, or do you have any specific questions?

### 5 Related Questions
1. How do you compute the row echelon form of a matrix?
2. What is the difference between row echelon form (REF) and reduced row echelon form (RREF)?
3. How can we determine if a set of vectors is linearly independent?
4. What are the implications of a matrix's rank in solving linear equations?
5. How does the rank of a matrix relate to its nullity?

**Tip:** Remember, the rank of a matrix is the dimension of the column space (or row space), which represents the number of linearly independent columns (or rows) in the matrix.

Learn how to determine the rank of a matrix A using row echelon form or reduced row echelon form (RREF). Understand the significance of matrix rank in linear algebra and applications. Detailed steps and examples provided.

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