1. The problem statement, all variables and given/known data Show that C[a; b], with the usual scalar multiplication and addition of functions, satises the eight axioms of a vector space. 2. Relevant equations Eight Axioms of Vector Space: A1. x + y = y + z A2. (x+y)+z=x+(y+z) A3. There exists an element 0 such that x + 0 = 0 A4. There exists an element -x such that x+(-x)=0 A5. α(x+y)=αx+αy A6. (α+β)x=αx+βx A7. (αβ)x=α(βx) A8. 1·x=x where x, y, and z are all vectors and α, β are scalars 3. 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?