, the answer works it out to not
It goes as follows: Set u = (u1, u2, u3), then (k+m)u = (k+m)(u1, u2, u3) = ((k+m)u1, (k+m)u2, (k+m)u3) and ku + mu = (ku1, ku2, ku3) + (mu1, mu2, mu3) = (ku3 + mu3, ku2 + mu2, ku1 + mu1)
since these are not equal, this axiom does not hold.'
Now, I don't understand why these two are not equal?
Can we not further simplify: (ku3 + mu3, ku2 + mu2, ku1 + mu1) = ((k+m)u3, (k+m)u2, (k+m)u1) ?
That way, does it not equal = ((k+m)u1, (k+m)u2, (k+m)u3)) ?
or is it not equal because the order of the triple is different?
I'm quite confused and any help would be much appreciated!
Have a great day all