If a homogeneous system has 6 equations and 5 unknowns, then there must be a unique
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These lines pass through the origin. Thus, there is always at least one solution, the point (0,0). ... A nxn homogeneous system of linear equations has a unique solution (the trivial solution) if and only if its determinant is non-zero. If this determinant is zero, then the system has an infinite number of solutions. I hope it help
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