Question Number 37225 by abdo.msup.com last updated on 11/Jun/18
![let n≥2 and f : R_n [x]→R_2 [x] / f(p) =xp(1) +(x^2 −4)p(0) 1) prove that f is linear 2) find dim Kerf and dimIm(f)](Q37225.png)
$${let}\:{n}\geqslant\mathrm{2}\:{and}\:{f}\:\::\:{R}_{{n}} \left[{x}\right]\rightarrow{R}_{\mathrm{2}} \left[{x}\right]\:/ \\ $$$${f}\left({p}\right)\:={xp}\left(\mathrm{1}\right)\:+\left({x}^{\mathrm{2}} \:−\mathrm{4}\right){p}\left(\mathrm{0}\right) \\ $$$$\left.\mathrm{1}\right)\:{prove}\:{that}\:{f}\:{is}\:{linear} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{dim}\:{Kerf}\:{and}\:{dimIm}\left({f}\right) \\ $$