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Laura1321412
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Homework Statement
Q) Determine if the set is a vector space under the given operations
The set of all pairs of real numbers of the form (1,x) with the operations (1,y)+(1,y')=(1,y+y') and k(1,y)=(1,ky)
2. Homework Equations / Solution Attempt
I know the axioms needed in this case, and I believe most all of them hold. The ones I am having trouble with in particular are
> There is an object 0 in V called the zero vector such that 0+u= u.
- But there isn't a zero vector if V is defined by (1,x) right?
> For each u in V there is an object -u in V, such that -u + u =0
- But -u would equal (1,-x) + (1,x) = (2,0) -- not 0
However, in the answer section of my book it says that this is a vector space under the given operations. I can't understand how the two above axioms hold... Any help is greatly appreciated!