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Math Help - linear mapping

  1. #1
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    Aug 2008
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    Cool linear mapping

    Hi,
    I posted this before but I think the formating was bad and I didn't get any help.
    I am attaching the problem this time with hope that someone can help me.

    Thank you so much![ATTACH]
    Attached Files Attached Files
    Last edited by ThePerfectHacker; September 18th 2008 at 06:42 PM.
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  2. #2
    Senior Member
    Joined
    Feb 2008
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    Quote Originally Posted by mivanova View Post
    Hi,
    I posted this before but I think the formating was bad and I didn't get any help.
    I am attaching the problem this time with hope that someone can help me.

    Thank you so much![ATTACH]
    Let's put this into LaTeX form:

    Let B_1={1,x,x^2,x^3,x^4} be the standard ordered basis of V. Let W be the vector space of 2x3 matrices over R with the usual addition of matrices and scalar multiplication. Let B_2 be the ordered basis of W given as follows:

    v_1=\left[\begin{array}{ccc} 1 & 0 & 0 \\ 0 & 0 & 0 \end{array}\right]

    v_2=\left[\begin{array}{ccc} 0 & 1 & 0 \\ 0 & 0 & 0 \end{array}\right]

    v_3=\left[\begin{array}{ccc} 0 & 0 & 1 \\ 0 & 0 & 0 \end{array}\right]

    v_4=\left[\begin{array}{ccc} 0 & 0 & 0 \\ 1 & 0 & 0 \end{array}\right]

    v_5=\left[\begin{array}{ccc} 0 & 0 & 0 \\ 0 & 1 & 0 \end{array}\right]

    v_6=\left[\begin{array}{ccc} 0 & 0 & 0 \\ 0 & 0 & 1 \end{array}\right]

    B_2=\left\{\begin{array}{cccccc}v_1&v_2&v_3&v_4&v_  5&v_6\end{array}\right\}

    Define T:\rightarrow W by:

    For f=a_0+a_1x+a_2x^2+a_3x^3+a_4x^4, put

    T(f)=\left[\begin{array}{ccc} 0 & a_3 & a_2+a_4 \\ a_1+a_0 & a_0 & 0 \end{array}\right]

    Construct the matrix A=[T]_{B_1,B_2} that represent T with respect to the pair B_1, B_2 of ordered bases.

    I have no idea what this is supposed to mean, though.
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