Results 1 to 3 of 3

Math Help - Linear Transformation Problem...

  1. #1
    Junior Member
    Joined
    Dec 2006
    Posts
    48

    Linear Transformation Problem...

    JUst need someone to showme how to do this then it will defintly clarify the rest of the problems for me.. one of the few examples is

    1- Show there exists a linear transofrmation T: R2→R3 such that T(1,1) = (1,0,2) and T(2,3) = (1,-1,4). What is T(8,11)?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    9
    Quote Originally Posted by ruprotein View Post
    JUst need someone to showme how to do this then it will defintly clarify the rest of the problems for me.. one of the few examples is

    1- Show there exists a linear transofrmation T: R2→R3 such that T(1,1) = (1,0,2) and T(2,3) = (1,-1,4). What is T(8,11)?
    You can express,
    [8,11]=2*[1,1]+3*[2,3]
    Using the linearity property of the linear operator to get,
    T(8,11)=2*T(1,1)+3*T(2,3)=2*[1,0,2]+3*[1,-1,4]
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by ruprotein View Post
    JUst need someone to showme how to do this then it will defintly clarify the rest of the problems for me.. one of the few examples is

    1- Show there exists a linear transofrmation T: R2→R3 such that T(1,1) = (1,0,2) and T(2,3) = (1,-1,4). What is T(8,11)?
    Suppose T is that thransformation

    T(1,0) = 3 T(1,1) - T(2,3) = (2, 1, 2)

    T(0,1) = T(2,3) - 2 T(1,1) = (-1,-1, 0)

    So the matrix M = (2, -1 ; 1, -1 ; 2, 0) does this job and so defines a linear
    transformation with the required properties, hence a linear transformation
    T exists with the required properties and is defined by the matrix M.

    Hence T(8,11) = [M (8,11)']' = (5, -3, 16)

    RonL
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. linear transformation problem
    Posted in the Advanced Algebra Forum
    Replies: 4
    Last Post: April 1st 2010, 03:13 AM
  2. Linear transformation problem
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: February 24th 2010, 04:11 AM
  3. Linear Transformation problem
    Posted in the Advanced Algebra Forum
    Replies: 7
    Last Post: February 6th 2010, 04:58 AM
  4. Linear transformation problem
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: July 17th 2008, 01:09 PM
  5. Linear Transformation problem
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: February 3rd 2008, 07:20 PM

Search Tags


/mathhelpforum @mathhelpforum