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x+y=0

2x+2y=0

This homogeneous system has infinitely many non-trivial solutions.

If you are looking for exactly one non-trivial solution, no such system exists. the system may or may not have non trivial solution. if number of variables equal to number of equations and given matrix is non singular then non trivial solution does not exist

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Q: Does any homogeneous system have nontrivial solution?
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