Not really the right place for that kind of algebra.
Look through your book. There is a numbered list of requirements to be a Vector Space. Find it and prove it - one requirement at a time.
By using the definition of vector space. But since you are already given that this is a set of vectors, you know that things like "associative law", etc. are true. What you need to do is see if, given that , [tex]v_3- v_4= 1[/itex], , and then the same is true of the sum . That is, is and . I recommend you look closely at that last equation!