if A is a square matrix(adsbygoogle = window.adsbygoogle || []).push({});

Ax = 0 has exactly one solution if and only if Ax = b has at least one solution for every vector b.

why is this true?

I am new to this if you can tell...

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

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

# Question Ax = 0 has only trivial solution and Ax = b has 1+ solution for every b

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