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Exercise 12

Avg difficulty 3.0

Consider this transformation of the plane R2\mathbb{R}^{2}.

(xy)↦(x/2y/3)\begin{pmatrix}x\\ y\end{pmatrix}\mapsto\begin{pmatrix}x/2\\ y/3\end{pmatrix}

Find the image under this map of this ellipse.

{(xy)∣(x2/4)+(y2/9)=1}\{\hskip 1.00006pt\begin{pmatrix}x\\ y\end{pmatrix}\mid(x^{2}/4)+(y^{2}/9)=1\hskip 1.00006pt\}

Hefferon, Linear Algebra, Maps Between Spaces, Definition, Exercise 12

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Adapted from Linear Algebra © 2016 Jim Hefferon. Licensed under CC BY-SA 3.0 US. Source: Linear Algebra. Imported at revision df2262e.