Provided a homogeneous system of equations (2), we will have one of the two probabilities for the number of solutions.

1.   Accurately one solution, the trivial solution

2.   Infinitely various non-zero solutions in addition to the trivial solution.

Under the second possibility we can say solution is non-zero since if there are moving to be infinitely many solutions and we identify that one of them is the trivial solution then all the rest should have at least one of the xi's be non-zero and thus we find a non-zero solution.