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Math Help - Linear transformation

  1. #1
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    Linear transformation

    Hello MHF,

    Consider the linear transformation
     T \left(\left[\begin{array}{cc}x_{1}\\x_{2}\end{array}\right]\right)=\left[\begin{array}{cc}3x_{1}+4x_{2}\\2x_{2}\end{array}\  right]

    (i) What is the standard matrix associated with this transformation.
    (ii) Consider the image of the unit disk under the transformation T. What is the area of this image?

    So I think that the standard matrix is just A = \left[\begin{array}{cc}3&4\\0&2\end{array}\right], but I am not sure what to do for part 2 of this question..
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  2. #2
    MHF Contributor

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    Quote Originally Posted by Robb View Post
    Hello MHF,

    Consider the linear transformation
     T \left(\left[\begin{array}{cc}x_{1}\\x_{2}\end{array}\right]\right)=\left[\begin{array}{cc}3x_{1}+4x_{2}\\2x_{2}\end{array}\  right]

    (i) What is the standard matrix associated with this transformation.
    (ii) Consider the image of the unit disk under the transformation T. What is the area of this image?

    So I think that the standard matrix is just A = \left[\begin{array}{cc}3&4\\0&2\end{array}\right], but I am not sure what to do for part 2 of this question..
    your answer to (i) is correct and for (ii) the answer is 6 \pi=|\det A| \times (\text{area of the unit circle}).
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