1
Question
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
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
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Solution
The correct option is D 0
Array is
⎡⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢⎣0−1−2⋯1−n10−1⋯210321⋮⋮⋮−(1−n)−(2−n)0⎤⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥⎦
Sum=0+1+2+...+(−1)+(−2)+...
=0
Array is
⎡⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢⎣0−1−2⋯1−n10−1⋯210321⋮⋮⋮−(1−n)−(2−n)0⎤⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥⎦
Sum=0+1+2+...+(−1)+(−2)+...
=0
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