Elem lin algebra (Vector space question)

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Miike012
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How is the following a vector space if it does not have a zero vector?
 
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  • Screenshot of textbook exercise 11: the set of pairs (1, y) with addition (1, y) + (1, y') = (1, y + y') and scalar multiplication k(1, y) = (1, ky), followed by the answer 'The set is a vector space with the given operations.' and a handwritten-style question asking whether there is a zero vector.
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If the space has a vector e such that x + e = x, for any vector x in the space, then e is acting as the zero vector. More formally, e is the additive identity.
 
Miike012 said:
but e = (0,0) is not of the form (1,x)

But for this vector space, e ≠ (0, 0).

What is e for this vector space?
 
Miike012 said:
is it (1,0)?
Yes, that's e .