Question

Evaluate $\left|\begin{array}{ccc}2009& 2010& 2011\\ 2010& 2011& 2012\\ 2011& 2012& 2013\end{array}\right|$

• A. $1$
• B. $-1$
• C. $0$
• D. $10$

Answer 1

The correct option is C $0$

Given,

$\left|\begin{array}{ccc}2009& 2010& 2011\\ 2010& 2011& 2012\\ 2011& 2012& 2013\end{array}\right|$

Applying the following transformations $C_3\to C_3-C_2;C_2\to C_2-C_1$

we get,

$\left|\begin{array}{ccc}2009& 2010& 2011\\ 1& 1& 1\\ 1& 1& 1\end{array}\right|$
Now, again doing $C_2\to C_2-C_3,$ we get

$\left|\begin{array}{ccc}2009& 2010& 2011\\ 0& 0& 0\\ 1& 1& 1\end{array}\right|$

Now, expanding along with $C_2$ we get

$\left|\begin{array}{ccc}2009& 2010& 2011\\ 0& 0& 0\\ 1& 1& 1\end{array}\right|=0$