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.