# Homework Help: Linear equation

1. Sep 11, 2011

### tk1234

Let a be a fixed nonzero vector in R^n

a. Show that the set S of all vectors x such at ax=0 is a subspace of R^n.
b. show that if k is a nonzero real number, then the set A of all vectors x such that ax=k is an affine subspace of R^n, but not a linear subspace.

how do i even show this.. im so confused. help please!! thanks.

Last edited: Sep 11, 2011
2. Sep 11, 2011

### Dick

Try?? Pretty please? Tell me what you might need to prove S is a subspace. You can look it up in the book if you want to. What's the definition of a subspace?

3. Sep 11, 2011

### tk1234

i know that S needs to be closed under addition and numerical multiplication.. im just not sure how to show this?!

4. Sep 11, 2011

### Dick

If x1 is in S then a.x1=0. If x2 is in S then a.x2=0. (I'm using '.' for dot product). Can you give me some reason why that would mean x1+x2 is in S? What would you have show to prove x1+x2 is in S? That would give you closure under addition.