Question

If the rank of the matrix \[ \begin{pmatrix} -1 & 2 & 5 \\ 2 & -4 & -4 \\ 1 & -2 & a + 1 \end{pmatrix} \] is 1, then the value of \( a \) is

• A. -1
• B. 2
• C. -6
• D. 4

Hint:

To find the rank of a matrix, compute the determinant and perform row reduction to check the number of linearly independent rows.

Answer 1

The Correct Option is C

Step 1: Using the rank condition.
The rank of a matrix is determined by finding the determinant and ensuring the matrix reduces to rank 1. Solving this gives \( a = -6 \).

Step 2: Conclusion.
Thus, the correct answer is option (C).

Final Answer: \[ \boxed{\text{(C) } -6} \]