od slavonija035 » Subota, 09. Februar 2013, 12:47
Ako je [inlmath]\left(e\right)=\left(\vec{e_1},\vec{e_2},\vec{e_3}\right)[/inlmath] ortonormirana baza vektorskog prostora [inlmath]V^3[/inlmath], pokažite da je [inlmath]\left(f\right)=\left(4\vec{e_1}+\vec{e_2}-\vec{e_3},\;-3\vec{e_1}+2\vec{e_2}+3\vec{e_3},\;\vec{e_1}-3\vec{e_2}-3\vec{e_3}\right)[/inlmath] baza istog vektorskog prostora. U bazi [inlmath]\left(f\right)[/inlmath] napišite matricu linearnog operatora [inlmath]A\colon V^3\to V^3[/inlmath] ako je [inlmath]A\left(x_1\vec{e_1}+x_2\vec{e_2}+x_3\vec{e_3}\right)=\left(x_1-x_3\right)\vec{e_1}+\left(2x_1+x_2+3x_3\right)\vec{e_2}+\left(x_2+2x_3\right)\vec{e_3}[/inlmath].