Question

The rank of the matrix \[ \begin{pmatrix} 1 & 2 & 5 \\ 2 & 4 & 4 \\ 3 & 6 & 6 \end{pmatrix} \] is

• A. 1 if \( a = 6 \)
• B. 2 if \( a = 1 \)
• C. 3 if \( a = 4 \)
• D. None of these

Hint:

The rank of a matrix is determined by the number of non-zero rows after applying row operations or calculating the determinant.

Answer 1

The Correct Option is A

By calculating the determinant or using row operations, we find that the rank of the matrix is 1 when \( a = 6 \).
Final Answer: \[ \boxed{1 \text{ if } a = 6} \]