Question

An $n\times n$ array V is defined as follow v[i,j] = i - j for all i, j, 1 $\le$ i, j $\le$ n then the sum of the elements of the array V is

• A. 0
• B. n - 1
• C. $n^2-3n+2$
• D. n ( n + 1 )

Answer 1

The correct option is A 0

Given that v[i,j] = i - j

Let n = 3

then $V_{3\times 3}=\left[\begin{array}{ccc}0& -1& -2\\ 1& 0& -1\\ 2& 1& 0\end{array}\right]$

Here the given matrix is skew symmetric matrix

Sum of all the elements of V=0