https://file.aiquickdraw.com/mathbot/file/17259817363051dj6uuvy.jpg

The matrix you uploaded appears to be:

\[
\begin{pmatrix}
1 & 2 & 3 & 4 \\
2 & 3 & 4 & 5 \\
3 & 4 & 5 & 6 \\
4 & 5 & 6 & 7
\end{pmatrix}
\]

This is a \(4 \times 4\) matrix. To find the rank of the matrix, we need to perform row reduction (Gaussian elimination) to bring the matrix into its row echelon form (REF) or reduced row echelon form (RREF) and count the number of non-zero rows.

Let's calculate it step by step. I will now perform the row reduction.The rank of the given matrix is \( 2 \). 

This means that the matrix has 2 linearly independent rows or columns, and thus its dimension is 2.

Would you like more details on how the row reduction process works, or do you have any other questions?

Here are five related questions to consider:
1. What is the difference between row echelon form and reduced row echelon form?
2. How is the rank of a matrix related to its determinant?
3. What does it mean if a matrix has full rank?
4. Can rank help in solving systems of linear equations?
5. How does rank relate to the invertibility of a matrix?

**Tip**: The rank of a matrix also tells you the maximum number of linearly independent vectors in the matrix's rows or columns.

Find rank of the matrix shown in the image.

Learn how to find the rank of a 4x4 matrix using Gaussian elimination and row echelon form. The rank of the matrix reveals the number of linearly independent rows or columns. This problem applies linear algebra concepts such as matrix theory and the Rank-Nullity Theorem.

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