Checking vector space axioms for triples with nonstandard scalar multiplication

[derryck1234]

Homework Statement

Show whether the set is a vector space: The set of all triples of real numbers (x, y, z) with the operations:

(x, y, z) + (x', y', z') = (x + x', y + y', z + z') and k(x, y, z) = (kx, y, z)

Homework Equations

(10 vector space axioms)

The Attempt at a Solution

I can understand 9 axioms, I just want to confirm that I am doing the right thing on this one:

(m + k)(x, y, z) = ((m+k)x, y, z), which is not equal to k(x, y, z) + m(x, y, z) = (kx, y, z) + (mx, y, z) = ((m+k)x, 2y, 2z).

Is this correct working?

Thanks

Derryck

 

[vela]

Yup.