1. ## subspaces

Hi,

How can I show that th set of all solutions to Ax = b where A is mxn, is not a subspace of R^n if b <> 0.

If Ax = 0, (b = 0), the set of solutions IS a subspace. What difference does it make whether b is 0 or not?

Thanks!

2. Originally Posted by kpizle
Hi,

How can I show that th set of all solutions to Ax = b where A is mxn, is not a subspace of R^n if b <> 0.

If Ax = 0, (b = 0), the set of solutions IS a subspace. What difference does it make whether b is 0 or not?

Thanks!

EDIT: Moving question to more appropriate forum
Suppose $x$ is a solution to this and $\lambda$ is a scalar, then $A(\lambda x)=\lambda b$, so $\lambda x$ is not in the set of solutions unless $b=0$, but if the set of solutions is a subspace it would have to be.

CB