Let V be the set of all positive real numbers. Define 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.

Printable View

- November 25th 2012, 05:48 AMalphaknight61Linear algebra problem
Let V be the set of all positive real numbers. Define 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.

- November 25th 2012, 05:57 AMcoolgeRe: 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).

- November 25th 2012, 10:08 AMPetrusRe: 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?

- November 25th 2012, 10:57 AMcoolgeRe: 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.

- November 26th 2012, 03:51 AMalphaknight61Re: 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!