Let F be the vector space of all functions mapping [tex] R [/tex] into [tex] R [/tex], and let [tex]T:F\rightarrow F[/tex] be a linear transformation such that [tex]T(e^{2x})=x^{2}[/tex], [tex] T(e^{3x})=sinx[/tex], and [tex]T(1)=cos5x[/tex]. Find the following, if it is determined by this data.(adsbygoogle = window.adsbygoogle || []).push({});

[tex]T(e^{5x})[/tex]

[tex]T(3e^{4x})[/tex]

[tex]T(3+5e^{3x})[/tex]

[tex]T(\frac{e^{4x}+2e^{5x}}{e^{2x}})[/tex]

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# Homework Help: Linear Algebra Problem

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