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Math Help - Linear transformation problem

  1. #1
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    Linear transformation problem

    Suppose that the linear transformation T maps \left[ \begin{bmatrix}1\\0 \end{bmatrix} \right] to \left[ \begin{bmatrix}2\\5 \end{bmatrix} \right] and \left[ \begin{bmatrix}0\\1 \end{bmatrix} \right] to \left[ \begin{bmatrix}-1\\6 \end{bmatrix} \right]

    Find T( \left[ \begin{bmatrix}x_1\\x_2 \end{bmatrix} \right])
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  2. #2
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    Unless I'm asleep and don't know it (which certainly could be the case), it's an eyeball problem.

    [2x_{1}-x_{2},5x_{1}+6x_{2}]^{T}
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  3. #3
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    Quote Originally Posted by tttcomrader View Post
    Suppose that the linear transformation T maps \left[ \begin{bmatrix}1\\0 \end{bmatrix} \right] to \left[ \begin{bmatrix}2\\5 \end{bmatrix} \right] and \left[ \begin{bmatrix}0\\1 \end{bmatrix} \right] to \left[ \begin{bmatrix}-1\\6 \end{bmatrix} \right]

    Find T( \left[ \begin{bmatrix}x_1\\x_2 \end{bmatrix} \right])

    Your told that the transformation is linear, you're given the images of the unit vectors i and j so can you determine a the 2by2 matrix to represent this transformation ? it quiet easy if you are unsure remember that the image of the i vectors tells you that \left(\begin{array}{cc}a & b \\c & d\end{array}\right) \times \left(\begin{array}{c}1 \\0\end{array}\right) = \left(\begin{array}{c}2 \\5\end{array}\right) you should easily be able to determine a, b c, and d.

    then T\left(\begin{array}{c}x_1 \\x_2\end{array}\right) = \left(\begin{array}{cc}a & b \\c & d\end{array}\right) \times \left(\begin{array}{c}x_1 \\x_2\end{array}\right)

    Bobak
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