Question

The value of the determinant –$\left| \begin{matrix} 10! & 11! & 12! \\ 11! & 12! & 13! \\ 12! & 13! & 14! \end{matrix} \right|$ equals –

• A. 2(10! 11!)
• B. 2(10! 13!)
• C. 2(10! 11! 12!)
• D. 2(11! 12! 13!)

Answer 1

Answer: (C)

2(10! 11! 12!)

Answer 2

10! 11! 12! $\left| \begin{matrix} 1 & 11 & 12 \times 11 \\ 1 & 12 & 13 \times 12 \\ 1 & 13 & 14 \times 13 \end{matrix} \right|$

R₃ → R₃ – R₂, R₂ → R₂ – R₁

= (10! 11! 12!) $\left| \begin{matrix} 1 & 11 & 12 \times 11 \\ 0 & 1 & 2 \times 12 \\ 0 & 1 & 2 \times 13 \end{matrix} \right|$ = 2 (10! 11! 12!)