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?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Solutions of Ax = b (for singular A)

**Physics Forums | Science Articles, Homework Help, Discussion**