Results 1 to 5 of 5

Math Help - Linear Transformations

  1. #1
    Member
    Joined
    Jul 2011
    Posts
    140

    Linear Transformations

    The question statement says find f(L), which I have highlighted in bold. However, the book's answer seems to continue on and calcualte for y from the f(L) equation, which I proceed to work out, although my final answer is slightly off. I'm slightly confused as to whether or not the highlihted value for f(L) is in fact f(L)! Can anyone help?

    Many thanks.

    Q.
    L is the line x - y + 1 = 0. f is the transformation f: (x, y) ---> (x', y') where: x' = 2x - y & y' = y. Find f(L).

    Attempt: If y = y', then x' = 2x - y => 2x = x' - y => 2x = x' - y' => x = \frac{x' - y'}{2}

    If L = x - y + 1 = 0, then f(L) = \frac{x' - y'}{2} - y' + 1 = 0 => x' - y' - 2y' + 2 = 0 => x' - 3y' + 2 = 0

    Now apply x/ y values to f(L) = x' - 3y' + 2 = 0 => 2x - y - 3y + 2 = 0 => 2x - 4y + 2 = 0 => x - 2y + 1 = 0 => 2y = x + 1 => y = \frac{x + 1}{2}

    Ans:
    (From text book): y = x + 2
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member
    Joined
    Mar 2012
    From
    Sheffield England
    Posts
    440
    Thanks
    76

    Re: Linear Transformations

    You have a sign wrong in first line of your attempt x'=2x-y gives 2x=x'+y
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Apr 2005
    Posts
    16,396
    Thanks
    1847

    Re: Linear Transformations

    Quote Originally Posted by GrigOrig99 View Post
    The question statement says find f(L), which I have highlighted in bold. However, the book's answer seems to continue on and calcualte for y from the f(L) equation
    I don't know what you mean by this. From the equation of the line, x- y+ 1= 0, y= x+ 1 so the set is {(x, x+1)}. Applying L to that we have x'= 2x- y= 2x- (x+ 1)= x- 1 and y'= y= x+ 1 so that (x, x+1) is mapped to (x- 1, x+ 1). If x'= x- 1 then x= x'+ 1 and x+ 1= x'+ 2, so we can also write this set as {(x', x'+ 2)}.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Senior Member
    Joined
    Mar 2012
    From
    Sheffield England
    Posts
    440
    Thanks
    76

    Re: Linear Transformations

    I just noticed that in the first line it said x'=2x-y => 2x=x'-y. I'm obviously not sure what f(L) means (?). I thought they were asking for the equation which the book gives.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Member
    Joined
    Jul 2011
    Posts
    140

    Re: Linear Transformations

    Thanks for the help. I'll give it a 2nd look.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Linear Transformations and the General Linear Group
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: December 26th 2011, 11:50 AM
  2. Linear Map transformations (Linear Algebra)
    Posted in the Algebra Forum
    Replies: 4
    Last Post: October 21st 2011, 10:56 AM
  3. Basic Linear Algebra - Linear Transformations Help
    Posted in the Advanced Algebra Forum
    Replies: 6
    Last Post: December 7th 2010, 04:59 PM
  4. Linear Algebra: Linear Transformations
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: December 9th 2008, 05:30 PM
  5. Replies: 3
    Last Post: June 2nd 2007, 11:08 AM

Search Tags


/mathhelpforum @mathhelpforum