Thread: Conditions for Vector Space

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 For and define,

and

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

Originally Posted by VS8

For each pair of elements in and each element in ,

I'm obviously missing something but I do not see how 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).

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



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

Thanks guys

In your example and . So means that .

Now,

and

.

So,