bamby

I can't. I know that the first one is a vector space and the second one is not but I can't prove it.

Can you, please help me with this problem? If these two operations are defined as follows. With these new definitions, is R3 a vector space? a) (x1, y1, z1)+(x2, y2, z2)=(x1 + x2 + 2, y1 + y2 + 2, z1 + z2 + 2) c(x, y, z)=(cx, cy, cz) b) (x1, y1, z1)+(x2, y2, z2)=(x1 + x2 + 4, y1 + y2 + 4, z1 + z2 + 4) c(x, y, z)=(cx + 4c – 4, cy + 4c – 4, cz + 4c – 4) Thanks!