- #1

sheldonrocks97

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## Homework Statement

Show that C[a; b], with the usual scalar multiplication

and addition of functions, satises the eight axioms of a vector space.

## Homework 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

## 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?