Results 1 to 6 of 6
Like Tree1Thanks
  • 1 Post By emakarov

Math Help - Is this a vector space

  1. #1
    Newbie
    Joined
    Dec 2012
    From
    Sri Lanka
    Posts
    3

    Is this a vector space

    A = {(x,y)| x,y belong R}
    scalar multiplication and addition are defined as
    a(x,y) = (ax,ay)
    (x1 , y1) + (x2 , y2) = (x1 + x2 + 1, y1+y2+1)

    1) can we define zero vector as (-1,-1)
    2) can we define -(x,y) as (-x-1,-y-1)
    3) is A a vector space
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Oct 2009
    Posts
    5,559
    Thanks
    785

    Re: Is this a vector space

    Good questions. Why don't you try answering them?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Apr 2005
    Posts
    16,241
    Thanks
    1795

    Re: Is this a vector space

    Your scalar mutiplication must satisfy a(u+ v)= au+ av. Is that true?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Dec 2012
    From
    Sri Lanka
    Posts
    3

    Re: Is this a vector space

    yes
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Dec 2012
    From
    Sri Lanka
    Posts
    3

    Re: Is this a vector space

    I don't see any reason why first and second statements are wrong.
    But the theorems -1u = -u and 0u = 0 contradicts my answer.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor
    Joined
    Oct 2009
    Posts
    5,559
    Thanks
    785

    Re: Is this a vector space

    Quote Originally Posted by HallsofIvy View Post
    Your scalar mutiplication must satisfy a(u+ v)= au+ av. Is that true?
    Quote Originally Posted by scnakandala View Post
    yes
    Please show us the proof.

    Quote Originally Posted by scnakandala View Post
    I don't see any reason why first and second statements are wrong.
    Let's see. "Can we define -(x,y) as (-x-1,-y-1)?" If yes, then -(x, y) + (x, y) = (-x - 1, -y - 1) + (x, y) = (-x - 1 + x + 1, -y - 1 + y + 1) = (0, 0). Have you done this computation? How does it square with the answer to question 1?

    The definition for unary minus can be adjusted so that -(x, y) + (x, y) = (-1, -1). However, post #3 points out a real problem.

    Quote Originally Posted by scnakandala View Post
    But the theorems -1u = -u and 0u = 0 contradicts my answer.
    Yes, -1(x, y) = (-x, -y) according by definition, but then -1(x, y) + 1(x, y) ≠ 0(x, y).
    Thanks from scnakandala
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Dual Space of a Vector Space Question
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: April 16th 2011, 04:02 AM
  2. Replies: 2
    Last Post: April 1st 2011, 03:40 AM
  3. Banach space with infinite vector space basis?
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: March 24th 2011, 07:23 PM
  4. Replies: 15
    Last Post: July 23rd 2010, 12:46 PM
  5. Isomorphism beetwenn vector space and sub space
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: November 30th 2008, 11:05 AM

Search Tags


/mathhelpforum @mathhelpforum