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Math Help - Transformations

  1. #1
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    Transformations

    If T maps \vec x into  \vec w, and the standard matrix is defined by the equations:
    w_1=2x_1-3x_2+x_3
    w_2=3x_1+5x_2-x_3

    How do I find the standard matrix? And then how do I find the image of vectors under T by substituting in the equations and using the standard matrix?

    The prof didn't go over any of this stuff, and yet still assigned one question as homework, and unfortunately the text is rather vague...
    Last edited by Hellreaver; November 12th 2008 at 03:19 PM.
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  2. #2
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    Your T is such that

    T\vec x = \vec w

    So

    T=\left[\begin{array}{ccc}2 & -1 & 1\\ 3 & 5 & -1 \end{array}\right]

    Check this.
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  3. #3
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    Alright so I kind of guessed that using some of the examples... But as for finding an image, all I would need to do is multiply the matrix you gave me with a matrix that substitutes for  x_1,x_2, and  x_3 correct?
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  4. #4
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    Yep For example, if x=(1,1,1) then Tx=(2,7)

    \left[\begin{array}{ccc}2 & -1 & 1\\ 3 & 5 & -1 \end{array}\right]\left[\begin{array}{c}1\\1\\1\end{array}\right]=\left[\begin{array}{c}2\\7\end{array}\right]
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  5. #5
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    Awesome, thanks so much.
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