Question

Given a vector V of size N, Find if there exists another vector A (of size N) such that A.V = 0 where . represents the Dot product or Inner Product ie a1*v1 + a2*v2 + a3 * v3 + … an*vn = 0, and A >0 ie all ai are non-negative integers and all ais cannot be 0 at the same time(trivial case).
Suggest an algorithm to generate a YES of NO.

Answer 1

Consider first the case when at least one of v_i = 0. Then it is easy for you to show that the answer is YES. Now move on to the cases where all the v_i ≠ 0. Now break this into two more subcases.

1. All the v_i have the same sign.
2. At least one pair, say v_i and v_j, i ≠ j , have different signs.

You should be able to complete the assignment from this breakdown.