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20 Sottoinsiemi

Study material for Analisi Matematica 2, shared by the Studwiz community and reviewed by moderators.

Analisi Matematica 2By topic

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13/03/2023 1)Stabilire,airequentiettoinsiemidiR3,rappresentano sottospazivettoriale: a)Fr= ((n,y,z)=R3:x= 0)CNSaffincheWCVsiaunattespaziovettorialediVechevalganoleagenticondizione:- i), Wite W i)WXeR,e xeW UngenericoelementodiFrlosceninellaforma.= [Et,NE i= [E]Tr=[E]ent,t +2-X []=[E)-, ew d'altraparteinexi= [][]t IèunsottospaziodiRE b)E= ((n,y,z)R:a+ y= x)x= - yUngenericoelementedi Tredatoda=[]=(att[8]t,1 a= -E]=FE]=T-EE] a)extitte=>us+Fa F - GE]= en= 0,+ Vz 11=xtx=[x]= [-]n= xw=xFa =>IèunsottospazòdiR3 inun'equazionelinearidellaformarautby+ct=0 rappresentaun panipassantepe(0,0,0)edeunsottospa_tiovettorialediR3. 3- {Y- Sc)Fz= ((x,y,z)-R3:x = y= z anelementodi Essara= [E]=[Itèunsottospaziodipesche+Na* = T]econlei;Do=Icande =>wiunarettapassanteaul'origine,definireun sottosportovettorialediR d)F4= ((x,y,z)-R:x = yvx= z]PresoanvettorediF.=I]eunvettorediFr 0= (5)i= [5]+ [3]= [e)EnonunsottospaziovettorialediR3 e)F5= ((x,y,z)-R.x= y+ 3)CNaffinchesiaunsottopaziodiRèche(P,0,0)EF5Ungenericoelementodi F5è= [t]= jetjut6] = []+]0+15]iBompaionoes f)Fg= F5u((0,0,0)EFo=[3]=[ta3]ett +- s R3I*E6Imanèunottapazòde ⑰g)Fg= ((n,y,z)c*:y=o⊥4(- y)(x+ y)=0 FF= ((My,z)tR3:ayvx=- y) =]=[5]EFeF +!=[8]*FF20 h)E= ((x,y,z)-R3:y= 2n,z= 3x)

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