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- Politecnico di Milano
- Degree programme
- Management Engineering
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- Analisi Matematica 2
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- Exercises · By topic
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ExercisesBy topic
01 Applicazione lineare
Study material for Analisi Matematica 2, shared by the Studwiz community and reviewed by moderators.
Analisi Matematica 2By topic
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EmI1FE)okFèun'applicazione=X unsytze =1 amore. 22/03/2023 1)Datala F.RaRstappeicazioneunire precedenR,a)sumerela matriceAche cappresenterI espettoalla vananonicalfiatoneldominienelcodominid e)studiareelimitità,laseriettivitàel'invertibilitàdiF DeterminareunabasedelRue(F)ediin(F)d)Caldarela dimensionediRee(F)ein(F) #(E)=eY-?-5e}F(e)= - 5esF(B)=es Fei)= []Fee)= [8]=(5)= (8) A= I1 0 I-100 -5-5b)perl'iniettivitàcaldoRueA:AR= . - 5- 51 - 5- 51 I [IEsoo- 28]I 0- 51v ~ 10 0 1 0- 51 21+ 53 - 5ry+ M1 -5- 51 - 5- 51 - 5x=t -tx=0 8- 5 ·[00][- 2)ty= 45t Der()()tt(RC)BRASIenveret bite).DallamatureadotteperMEG,deducethee(A)=2dim(m)F)=23:unabasedell'in(F)èdatoda: Blmcr= 7[],[8]}d)Rer(F)iim(F) SetReIF)r(I)accora= [5]aaR []a= a]+ as[i] *= 58- 45 -5-- x= 5I1 -5- 1I - 5 I↑ ↑4 1,+ 53 - 522+ 41Oz&1 - 5 - 1 0 - 5-1 ites - 5 I0-5 8 - 1 e(M))=3 a,= ay= az= 0 =kve(F)1im(FIESO=0 dein(erFinF)=0 2)SiaD:Pm*Pml'applicazionecheassocioadognipolinomiola suorderatafreniaa)DimostrarecheDèun'applicazioneancore a)Postom= 3,evenirelamatricerappresentativerdiD espettoalla basedeimonomisudominioecodominio c)semprenelcasom=3 determinariela dimensionee unabasedelRer(D)em(D).Siciconacono geispaziridicate: a)siaiqualunqueeAmtMR(m+1,mila matricerap-presentativo:diDalvararidim.Dimostrareche,comun quesceltom,eateininterep=p(m)=Ataleche Am=0 tp>,q. a)f:RYRf(IT)= f(x)+ f(*)tr,eRNVXER f(xE=xfo 3=> fazio↓2,3-Rf(x+ B)= 2f(n)+ Bf(0))Siancp,qt4m<p+Bqcon x,ptRD(xp+ Bq)= (xp+ Bq)=xp+ Bp= 2D(p)+ BD(a)ok dalleproprietàdelladurata h)B= (x,x,x,z)p(x)=ax+ban+d D(1)=0 = 587mismoauc,eR"
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