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Math Help - Finding eigenvalues

  1. #1
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    Finding eigenvalues

    The following is an exercise that my professor gave us. I am confident that I can solve it but I'm not sure how to interpret T^2v.

    Exercise: Suppose the linear map T:\mathbb{R}^2 \rightarrow \mathbb{R}^2 is given by T(a,b)=(a+4b,3a+5b).
    Let v=(2,1). Find coefficients a_0,a_1,a_2 so that a_{0}v+a_{1}Tv+a_{2}T^{2}v=0.
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  2. #2
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    Quote Originally Posted by zebra2147 View Post
    The following is an exercise that my professor gave us. I am confident that I can solve it but I'm not sure how to interpret T^2v.

    Exercise: Suppose the linear map T:\mathbb{R}^2 \rightarrow \mathbb{R}^2 is given by T(a,b)=(a+4b,3a+5b).
    Let v=(2,1). Find coefficients a_0,a_1,a_2 so that a_{0}v+a_{1}Tv+a_{2}T^{2}v=0.
    T^2v means T(T(v)), so that

    T^2(a,b)=T(T(a,b))=T(a+4b,3a+5b)
    =(a+4b+4(3a+5b),3(a+4b)+5(3a+5b))
    =(13a+24b,18a+37b).
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