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In the definition of the solution set of Homogeneous systems in Wikipedia it is written:

Every homogeneous system has at least one solution, known as the zero solution (or trivial solution), which is obtained by assigning the value of zero to each of the variables. If the system has a non-singular matrix (det(A) ≠ 0) then it is also the only solution. If the system has a singular matrix then there is a solution set with an infinite number of solutions

But "If the system has a singular matrix then there is a solution set with an infinite"? does it need to be just one? just the zero solution as written in the properties of invertible matrix

The equation Ax = 0 has only the trivial solution x = 0

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    $\begingroup$ Wikipedia is correct. Non-singular is the same as invertible. $\endgroup$ Dec 14, 2014 at 4:44
  • $\begingroup$ @RobertIsrael ahh sorry may bad $\endgroup$
    – gbox
    Dec 14, 2014 at 4:45

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The word "singular" means "non-invertible". So the fact that $Ax=0$ has only the trivial solution $x = 0$ when $A$ is invertible is irrelevant to the statement

If the system has a singular matrix then there is a solution set with an infinite number of solutions

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