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Math Help - Linear Transformations

  1. #1
    Member akhayoon's Avatar
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    Linear Transformations

    I looked everywhere in the book for answer for this kind of question and they don't have it.

    all they have is the easy case where T[1 0] and T[0 1]

    it's in the attachment below
    Attached Thumbnails Attached Thumbnails Linear Transformations-untitled.jpg  
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by akhayoon View Post
    I looked everywhere in the book for answer for this kind of question and they don't have it.

    all they have is the easy case where T[1 0] and T[0 1]

    it's in the attachment below
    Well, solve
    \left ( \begin{matrix} a & b \\ c & d \end{matrix} \right ) \left ( \begin{matrix} 1 \\ 1 \end{matrix} \right ) = \left ( \begin{matrix} 3 \\ -2 \end{matrix} \right )

    and

    \left ( \begin{matrix} a & b \\ c & d \end{matrix} \right ) \left ( \begin{matrix} 1 \\ -1 \end{matrix} \right ) = \left ( \begin{matrix} 1 \\ 5 \end{matrix} \right )

    for a, b, c, and d.

    After you get that, see if
    Tx + Ty = T(x + y)
    where x and y are arbitrary column vectors.

    -Dan
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