Hey guys,

After a 3 year hiatus from taking any math courses i'm now taking an intermediate lin alg course and im a bit slow; I say this because I dont want you guys to hurt me for asking something so easy

In my text it gives an example of,

Let $\displaystyle S =\{ (a_1 , a_2): a_1 , a_2 \in R \} $ For $\displaystyle (a_1 , a_2), (b_1 , b_2) \in S $ and $\displaystyle c \in R $ define,

$\displaystyle (a_1 , a_2) + (b_1 , b_2) = (a_1 + b_1, a_2 - b_2) $ and $\displaystyle c(a_1, a_2) = (ca_1, ca_2) $

All is well, and the example goes on to say that the situation described above violates the commutatively of addition and the associativity of addition, which I agree. But it also says it violates VS8 (so it is therefore not a vector space), which is

I'm obviously missing something but I do not see how $\displaystyle c(a_1, a_2) = (ca_1, ca_2) $ violates the above condition. It actually makes sense that this is the case to me. If i have a physical vector and I multiply it by a scalar both its points should be multiplied by the scalar (I use a physical vector as an exmaple here I do know that vectors are not just physical).Originally Posted byVS8

Also, the next example takes the same situation but with the definition of

$\displaystyle c(a_1, a_2) = (ca_1, 0) $

And this situation does not violate VS8. But i cannot see why, so clearly I am missing something with the VS8 condition!

Thanks guys