Syed Islam

2022-07-20

Determine whether the following set equipped with the given operations is a vector space. If not vector spaces identify the vector space axioms that fail. 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)

Jeffrey Jordon

Expert

Not a vector space because the scalar multiplication is not hold.

If we Put k=0 then according to the definition of vector space

but in this case

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