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:

• A. 1
• B. 2
• C. 3
• D. 4

Hint:

The rank of a matrix is the number of non-zero rows in its row echelon form.

Answer 1

The Correct Option is C

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: \[ \boxed{3}. \]