Thread: 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!

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 is a solution to this and is a scalar, then , so is not in the set of solutions unless , but if the set of solutions is a subspace it would have to be.

CB