[Math] Is the solution space of a homogeneous linear system the same as the null space

linear algebra

Is the solution space of a homogeneous linear system the same as the null space?

If not how do they differ?

(sorry if this is a really stupid question)

Best Answer

That's pretty much correct, all I would do is to make a slight correction to your mathematical grammar. Given a homogeneous linear system of equations written as a matrix equation $MX=0$, the solution space of the system is the same as the null space of the matrix $M$.