Question

if a is a n x m matrix, b is an arbitrary vector in rn, then the set of vectors x in r^m such that ax=b is a subspace of rm

true or false, why?

Answer 1

False.

Answer 2

I have true for the solution

Answer 3

sorry i mistyped

Answer 4

If A is a n x m matrix, then the set of vectors x in R^m such that Ax=0 is a subspace of R^m.

Answer 5

Now, it is true

Answer 6

because that subspace is kernel A