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Exercise 2

Avg difficulty 3.0

For the map f ⁣:P1→R2f\colon\mathcal{P}_{1}\to\mathbb{R}^{2} given by

a+bx⟼f(a−bb)a+bx\stackrel{{\scriptstyle f}}{{\longmapsto}}\begin{pmatrix}a-b\\ b\end{pmatrix}

Find the image of each of these elements of the domain.

  • (a)  3−2x3-2x     (b)  2+2x2+2x     (c)  xx

Show that this map is an isomorphism.

Hefferon, Linear Algebra, Maps Between Spaces, Definition and Examples, Exercise 2

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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.