Aplicaciones lineales (1)
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Transcript of Aplicaciones lineales (1)
![Page 1: Aplicaciones lineales (1)](https://reader034.fdocumento.com/reader034/viewer/2022042514/55d033febb61eb862b8b47e7/html5/thumbnails/1.jpg)
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Sean las Bases de R3:
a) Hallar la matriz Q=.
1) (1,0,0) ā f (1,0,0)= (1,0,0)= Ī± (1,1,1) + Ī² (1,1,0) + Ļ (1,0,0)2) (0,1,0) ā f (0,1,0)= (0,1,0)=Ī± (1,1,1) + Ī² (1,1,0) + Ļ (1,0,0)3) (0,0,1) ā f (0,0,1)= (0,0,1)= Ī± (1,1,1) + Ī² (1,1,0) + Ļ (1,0,0)
![Page 3: Aplicaciones lineales (1)](https://reader034.fdocumento.com/reader034/viewer/2022042514/55d033febb61eb862b8b47e7/html5/thumbnails/3.jpg)
F1 ā F3 F2 ā F2 ā F1 F3 ā F3 ā F2
F3 ā F3 ā F1
Ī±= 0; Ī²=0; =1. Ī±= 0; Ī²=1; =-1. Ī±= 1; Ī²=-1; =0.
Q==
![Page 4: Aplicaciones lineales (1)](https://reader034.fdocumento.com/reader034/viewer/2022042514/55d033febb61eb862b8b47e7/html5/thumbnails/4.jpg)
b) Hallar
1) (1,1,1) ā (1,1,1)= (1,1,1)= (1,0,0) + (0,1,0) + (0,0,1)
2) (1,1,0) ā (1,1,0)= (1,1,0)= (1,0,0) + (0,1,0) + (0,0,1)
3) (1,0,0) ā (1,0,0)= (1,0,0)= (1,0,0) + (0,1,0) + (0,0,1)
![Page 5: Aplicaciones lineales (1)](https://reader034.fdocumento.com/reader034/viewer/2022042514/55d033febb61eb862b8b47e7/html5/thumbnails/5.jpg)
P==
c) Verificar que P= Q-1.
![Page 6: Aplicaciones lineales (1)](https://reader034.fdocumento.com/reader034/viewer/2022042514/55d033febb61eb862b8b47e7/html5/thumbnails/6.jpg)
F1 ā F3 F1 ā F1 + F2
![Page 7: Aplicaciones lineales (1)](https://reader034.fdocumento.com/reader034/viewer/2022042514/55d033febb61eb862b8b47e7/html5/thumbnails/7.jpg)
F2 ā F2 + F3
F1 ā F1 + F3
![Page 8: Aplicaciones lineales (1)](https://reader034.fdocumento.com/reader034/viewer/2022042514/55d033febb61eb862b8b47e7/html5/thumbnails/8.jpg)