Question

The value of $\left|\begin{array}{ccc}1990& 1991& 1992\\ 1991& 1992& 1993\\ 1992& 1993& 1994\end{array}\right|$ is equal to

• A. 1992
• B. 1993
• C. 1994
• D. 0

Answer 1

Answer: (D)

0

$A=\left|\begin{array}{ccc}1990& 1991& 1992\\ 1991& 1992& 1993\\ 1992& 1993& 1994\end{array}\right|$

$R_2\to R_2-R_1$ and $R_3\to R_3-R_2$

So,$A=\left|\begin{array}{ccc}1990& 1991& 1992\\ 1& 1& 1\\ 1& 1& 1\end{array}\right|$

So, two rows of det A are same.

So, $detA=0$