Question

If $\left| \begin{matrix} x & 3 & 6 \\ 3 & 6 & x \\ 6 & x & 3 \end{matrix} \right| = \left| \begin{matrix} 2 & x & 7 \\ x & 7 & 2 \\ 7 & 2 & x \end{matrix} \right| = \left| \begin{matrix} 4 & 5 & x \\ 5 & x & 3 \\ x & 4 & 5 \end{matrix} \right| = 0$ = 0 then x is

equal to

• A. 9
• B. -9
• C. 0
• D. None of these

Answer 1

Answer: (B)

-9

Answer 2

By circulant determinant property a + b + c = 0 ⇒ x + 3 + 6

= x + 2+ 7 = x + 4 + 5 = 0 ⇒ x = -9 .