Question

Consider a 2 - D array A[ ][ ] which represents a matrix having same no. of rows and columns. Let the no. of rows be n then the size of the matrix that the array A[ ][ ] represents is $n\times n$. The array elements are such that the value at each location is equivalent to the difference between the column number and the row number. It is represented as follows : A[p][q] = p - q, where $1\le p\le n$ and $1\le q\le n$. What would be the sum of the elements of the matrix representation of array A[ ][ ]?

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

Answer 1

The correct option is A 0

Given a 2 - D array A[ ][ ] is a representation of $n\times n$ matrix, where : Prep [p][q] = p - q
$A\left[i\right]\left[j\right]=\left[\begin{array}{cccc}0& -1& ....& 1-n\\ 1& 0& ....& \\ 2& 1& ....& \\ -(1-n)& -(2-n)& ....& O\end{array}\right]$

Sum of A[p][q] = 0 + 1 + 1 ....+ (-1) + (-2) ...
Sum if A[p][q] = 0