Hello,
It's quite strange, because v1=-v2, so (v1,v2,v3) can't be a basis of R3
1. v1 and v2 are independent and therefore by definition cannot be part of a basis. At best, the set of vectors span. But .....
2. The set of vectors do not span. eg. You cannot construct any vector of the form (a, 0, 0) from them.
Alternatively, the dimension of the set of vectors is 2 (since only two of them are independent). But the dimension of R3 is ...... well, 3.
There has to be a typo. I suggest you discuss this with your professor.