Show that C[a; b], with the usual scalar multiplication
and addition of functions, satises the eight axioms of a vector space.
Eight Axioms of Vector Space:
A1. x + y = y + z
A3. There exists an element 0 such that x + 0 = 0
A4. There exists an element -x such that x+(-x)=0
where x, y, and z are all vectors and α, β are scalars
The Attempt at a Solution
Let x=<1,2,3> y=<4,5,6> and z=<7,8,9> α=2 and β=3
1. <1,2,3>+<4,5,6>=<5,7,9> and <4,5,6>+<1,2,3>=<5,7,9>
Am I on the right track here or is there something I am doing wrong so far?