Álgebra Lineal EPN
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Transcript of Álgebra Lineal EPN
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ESCUELA POLITÉCNICA
NACIONALAlgebra Lineal
![Page 2: Álgebra Lineal EPN](https://reader031.fdocuments.mx/reader031/viewer/2022020102/55d0339fbb61eb8b2b8b479d/html5/thumbnails/2.jpg)
Dada la transformación lineal f: R2 P2(t) donde B1={(1,-1),(1,1)}, B2={(1-t,2,1+t-t2)}, son bases de R2 y P2(t) respectivamente. Además, C representa las bases canónicas de R2 y P2 (t).
a)Determinar f explícitamente si =
b)Encontrar
c)Encontrar
d)Determinar si f es biyectiva
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a)
C={(1,0),(0,1)}
C={1,t, t2}
[f()]B2=A[]B1
F2=F2+F1 F2=F2/2 F1=F1-F2
[]c=
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[f()]c2=A[]c1
[f()]c2=
=
f()=(a-b)(1-t)+(2a-2b)(2)-(b)(1+t- t2 )
f()=(a-b-at+bt)+(4a-4b)-(b+bt-bt2 )
f()=(a-b-at+bt+4a-4b-b-bt+bt2 )
f()=(5a-6b)-a+bt2
f(a,b)=(5a-6b)-a+bt2
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b)Encontrar
f(u1)=2+4t-t2
f(u2)= t2
2+4t- t2=(1-t)+2+(1+t+ t2)
+2 +=2
- +=4
=-1
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b)Encontrar
F2= F2+F1 F2= F2/2
F1=F1-F3 F1=F1-2F2 F2= F2- F3
.·. =
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c)Encontrar
2+4t- t2=+ t + t2
=2
=4
=-1
=
d)Determinar si f es biyectiva
Dim P2 (t)
2=3
.·. no es biyectiva
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GRACIAS