# Linear algebra problem

• Nov 25th 2012, 04:48 AM
alphaknight61
Linear algebra problem
Let V be the set of all positive real numbers. De fine α + β = αβ - 1 and c(α) = α . For example, 5 + 6 = (5)(6) - 1 = 29 and 3(7) = 7. Is V a vector space or not? Support your answer.
• Nov 25th 2012, 04:57 AM
coolge
Re: Linear algebra problem
No It is not a vector space. Associative property of addition is not satisfied. (a + b) + c is not equal to a+(b+c).
• Nov 25th 2012, 09:08 AM
Petrus
Re: Linear algebra problem
Wait assciotive law says for Matrices a+(b+c)=(a+b)+c so it should be same backwoord??? ( i have just studdy Matrices and dont know alot but that what ik, im not in Vector) coolge are u sure?
• Nov 25th 2012, 09:57 AM
coolge
Re: Linear algebra problem
Yes. Matrix addition is associative. But the question posted is not on the space of matrices. There V is a set where the addition operation is defined in a specific way. Under that operation V is not associative.
• Nov 26th 2012, 02:51 AM
alphaknight61
Re: Linear algebra problem
Yes coolge,matrix addition is associative however I limit my question to only vertices. But, can you show me a proof showing that associative property does not apply? sorry just confused how to apply the law of associativity in terms of vertices. thank you!