There are

ways of pairing up any 2 members from the pool of
contestants. Note that

so that

Explanation:
Since {v1,...,vp} is linearly dependent, there exist scalars a1,...,ap, with not all of them being 0 such that a1v1+a2v2+...+apvp = 0. Using the linearity of T we have that
a1*T(v1)+a2*T(v1) + ... + ap*T(vp) = T(a1v19+T(a2v2)+...+T(avp) = T(a1v1+a2v2+...+apvp) = T(0) = 0.
Since at least one ai is different from 0, we obtain a non trivial linear combination that eliminates T(v1) , ..., T(vp). That proves that {T(v1) , ..., T(vp)} is a linearly dependent set of W.
Answer:
104, 106
Step-by-step explanation:
Hello!
A consecutive number is a number that comes after the other.
Let the first even integer be x. Since there is an even integer for every two integers, the second number should be x + 2.
<h3>Solve for x</h3>
- (x) + (x + 2) = 210
- x + x + 2 = 210
- 2x + 2 = 210
- 2x = 208
- x = 104
The second number is x + 2, so it would be 106.