Question

$\left|\begin{array}{ccc}10!& 11!& 12!\\ 11!& 12!& 13!\\ 12!& 13!& 14!\end{array}\right|=$

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

Answer 1

Answer: (B)

$\left|\begin{array}{ccc}1& 1& 1\\ 11& 12& 13\\ 11.12& 12.13& 13.14\end{array}\right|$
$=10!11!12!\times \left|\begin{array}{ccc}1& 0& 1\\ -1& -1& 13\\ -24& -26& 13.14\end{array}\right|$
$10!11!12!(26-24)=2.10!11!12!$