In the Following Question: The set of all ordered triples of real numbers with the operations
$(x, y, z) (+) (x', y', z') = (x +x' , y + y', z + z')$
$r(*)(x, y ,z)=(x,1,z)$
Now Since the addition is standard addition, it should follow all the addition axioms. But I can't seem to figure out it's additive inverse.
I found the additive identity as (0,0,0)
But when I take additive inverse of $V = (x,y,z)$
$-V = (x,1,z)$ according to the multiplication given; adding it to $V$ gives result of $(2x,2,2z)$ which is not equal to additive identity.
P.S $(+)$ and $(*)$ represents vector addition and Vector Multiplication, I didn't know how to format them and I know that it doesn't form the vector space per se multiplication axioms but I still want to know how to find it's additive inverse. Thank you