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Answer :
Final answer:
To find the rank of the 5x5 matrix provided, Gaussian elimination would be used, but the pattern within the matrix implies that the rows are linearly dependent, indicating a rank of 1.
Explanation:
The matrix is a 5x5 matrix with elements following a regular pattern, where each row and column is increasing by 1. To determine the rank, one would typically perform Gaussian elimination to determine the number of non-zero rows in its row-echelon form.
However, the pattern in this matrix suggests that the rows are linearly dependent (each row is obtained by adding 1 to the previous row), indicating that the rank is less than 5. Since there's at least one non-zero row, the rank must be at least 1.
A typical approach would involve reducing the matrix to a simpler form to clearly identify the number of linearly independent rows, but the regular pattern here strongly suggests the rank is 1, as each row can be generated from the other by linear combinations.
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