A system of linear equations, Ax = b (with A a square matrix), has a unique solution iff [tex]det(A) \ne 0[/tex]. If b = 0, the system is homogeneous and can be solved using SVD (which gives the null space of A).(adsbygoogle = window.adsbygoogle || []).push({});

Now, how can the solution set be characterized for singular A and [tex]b \ne 0[/tex]? If a single solution [tex]s[/tex] is known, [tex]s + v[/tex] is also a solution for all [tex]v[/tex] from the null space of A... but how is it possible to determine whether such an [tex]s[/tex] exists at all, and if so, find it?

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# Solutions of Ax = b (for singular A)

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