Suppose that vectors x and y are both in the linear span of the
vectors r1, r2, r3. Show that any linear combination of x and y is also
in the linear span of r1, r2, r3.
What I have-
Because x and y are in the span of r1,r2,r3, then x and y are linear combinations of r1,r2,r3. So, the following exists:
c1(r1)+c2(r2)+c3(r3) = x
d1(r1)+d2(r2)+d3(r3) = y
where the d's and c's are scalars. I'm not sure this gets me anywhere with the proof.