Question:
The rank of the matrix \( \begin{bmatrix} 5 & 0 & -5 & 0 \\ 0 & 2 & 0 & 1 \\ -5 & 0 & 5 & 0 \\ 0 & 1 & 0 & 2 \end{bmatrix} \) is:
The rank of the matrix \( \begin{bmatrix} 5 & 0 & -5 & 0 \\ 0 & 2 & 0 & 1 \\ -5 & 0 & 5 & 0 \\ 0 & 1 & 0 & 2 \end{bmatrix} \) is:
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The rank of a matrix is the number of non-zero rows in its row echelon form.
Updated On: Dec 20, 2025
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The Correct Option is C
Solution and Explanation
To determine the rank of the matrix, we can perform Gaussian elimination (row reduction) to bring the matrix to row echelon form. After applying row operations, we find that the matrix has 3 non-zero rows, so the rank of the matrix is 3.
Final Answer: \[ \boxed{3}. \]
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