Results 1 to 5 of 5

Math Help - Linear Transformation

  1. #1
    Member
    Joined
    Nov 2006
    Posts
    142

    Linear Transformation

    I have to solve the following problem:

    Let V be the R-space of real polynomials of degree at most 3.
    For p(X) in V, define

    Tp(X)=1/6(19-6x+7x^2+32x^3-15x^4-6x^5)p'''(X)+(6-7x-9x^2+5x^3+x^4)p''(X)+(7-5x^2+2x^3)p'(X)+(10-6x^2)p(X).

    Find [T]s where S is the standard ordered basis {1,x,x^2,x^3}.
    Find [T]b where B is the non-standard ordered basis {2-12x-x^2+4x^3, 2-x^2, 3-x^2, -5x+2x^3}.

    How do I work these out?
    Last edited by PvtBillPilgrim; January 31st 2007 at 09:00 AM.
    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 PvtBillPilgrim View Post
    I have to solve the following problem:

    Let V be the R-space of real polynomials of degree at most 3.
    For p(X) in V, define

    Tp(X)=1/6(19-6x+7x^2+32x^3-15x^4-6x^5)p'''(X)+(6-7x-9x^2+5x^3+x^4)p''(X)+(7-5x^2+2x^3)p'(X)+(10-6x^2)p(X).

    Find [T]s where S is the standard ordered basis {1,x,x^2,x^3}.
    Find [T]b where B is the non-standard ordered basis {2-12x-x^2+4x^3, 2-x^2, 3-x^2, -5x+2x^3}.

    How do I work these out?
    If T:V\to W
    And B=\{v_1,...,v_n\}
    And B'=\{w_1,...,w_m\}
    Are the relative bases then,
    [T]_{B' B}=[[T(v_1)]_{B'}|[T(v_2)]_{B'}|...|[T(v_n)]_{B'}]
    Where the "||" are the adjoining the coloum vectors to the matrix.
    That is the formula, the answer and solution might be long. These things get very computational. But that is the procedure that is used.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Nov 2006
    Posts
    142
    I think I need to assemble Tp(X) into a matrix. How do I do this?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    9
    Quote Originally Posted by PvtBillPilgrim View Post
    I think I need to assemble Tp(X) into a matrix. How do I do this?
    You find the transformations of the basis vectors.
    Then you find their respective coordinate vectors relative to the second base.
    Then the matrix obtained by the cololum coordinate vectors is the standard matrix for the linear transformation.
    (That was the same thing I wrote only in nota
    tion)
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Member
    Joined
    Nov 2006
    Posts
    142
    We took some simple example like y=(2/3)x and it became the matrices:

    3 -2
    2 , 3
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: August 1st 2011, 10:00 PM
  2. Example of a linear transformation T:R^4 --> R^3?
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: April 5th 2011, 07:04 PM
  3. linear transformation
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: October 28th 2009, 06:40 AM
  4. Linear Algebra.Linear Transformation.Help
    Posted in the Advanced Algebra Forum
    Replies: 4
    Last Post: March 5th 2009, 01:14 PM
  5. Linear Transformation
    Posted in the Pre-Calculus Forum
    Replies: 10
    Last Post: May 25th 2008, 12:14 AM

Search Tags


/mathhelpforum @mathhelpforum