As far as this topic is concerned, it can be seen from the topic that vectors a and b are a set of bases, so. Any vector m on the plane can be represented by vectors a and b, that is, there are real numbers x and y, which makes m=xa+yb hold.

It can be seen that as long as X and Y exist, there are no other special requirements.

Actually, the vector 0=0a+0b.

It can be seen that vector M can be represented by vectors A and B, but it is a necessary and sufficient condition that both X and Y are not zero.

So the red line part is completely unnecessary.

Besides, you don't have to bother about this problem. You can completely regard A and B as equations about e 1 and e2, solve the formulas of e 1 and e2 about A and B, and substitute c=e 1+3e2 to avoid your confusion.