An n × n array v is defined as follows: v[i, j] = i − j for all i, j, 1 <= i…

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An n × n array v is defined as follows:

v[i, j] = i − j for all i, j, 1 <= i <= n, 1 <= j <= n

The sum of the elements of the array v is

  1. A.

    0

  2. B.

    n−1

  3. C.

    n² − 3n + 2

  4. D.

    n²(n+1)/2

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Correct answer: A

The sum of the array elements can be calculated by splitting the double summation into two parts. Since the term i appears n times and j appears n times symmetrically, they cancel each other out completely. Therefore, the total sum of all elements in the n × n array is exactly zero.

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