Determine whether the following set equipped with the given operations is a vector space. If...

Syed Islam

Syed Islam

Answered

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)

Answer & Explanation

Jeffrey Jordon

Jeffrey Jordon

Expert

2022-11-07Added 2575 answers

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

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

but in this case

0(1,y)=(1,0)  (0,0)

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