Results 1 to 2 of 2

Math Help - Linear algebra question

  1. #1
    Junior Member
    Joined
    Dec 2006
    Posts
    28

    Linear algebra question

    If anyone could explain how the following is done, it would be greatly appreciated!

    *Note that (+) denotes the vector addition symbol (which is displayed in textbooks as a circle with a plus sign inside it)

    Here is a vector space candidate. We have as our set, R^2, as our vector addition x (+) y = (x1, x2) (+) (y1, y2) = (x1y1, x2y2) and as our scalar multiplication a * x = a * (x1, x2) = (a + x1, a + x2). Verify the following vector space axiom.

    a * (x (+) y) = (a * x) (+) (a * y)
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    9,664
    Thanks
    298
    Awards
    1
    Quote Originally Posted by faure72 View Post
    If anyone could explain how the following is done, it would be greatly appreciated!

    *Note that (+) denotes the vector addition symbol (which is displayed in textbooks as a circle with a plus sign inside it)

    Here is a vector space candidate. We have as our set, R^2, as our vector addition x (+) y = (x1, x2) (+) (y1, y2) = (x1y1, x2y2) and as our scalar multiplication a * x = a * (x1, x2) = (a + x1, a + x2). Verify the following vector space axiom.

    a * (x (+) y) = (a * x) (+) (a * y)
    Let x be the point (b, c) and y the point (d, e).

    Then
    x (+) y = (bd, ce)
    a * (x (+) y) = (a + bd, a + ce)

    Now
    a * x = (a + b, a + c)
    a * y = (a + d, a + e)

    (a * x) (+) (a * y) = ((a + b)(a + d), (a + c)(a + e))

    = (a^2 + (b + d)a + bd, a^2 + (c + e)a + cd)

    I can't see how the two can be equal if x and y belong to R^2 without some other restriction.

    -Dan
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Linear Algebra: Linear Independence question
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: May 3rd 2011, 05:28 AM
  2. Linear Algebra question
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: November 22nd 2009, 04:08 AM
  3. Linear Algebra Question - Linear Operators
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: March 3rd 2009, 04:33 AM
  4. linear algebra question
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: October 16th 2008, 07:08 PM
  5. Linear algebra question...
    Posted in the Algebra Forum
    Replies: 1
    Last Post: September 30th 2007, 10:25 PM

Search Tags


/mathhelpforum @mathhelpforum