## Question

###### Considcr thc matrix:Compute all eigcnvalucsandl thcir eigenvectors ViMATk?Give Ilalrix F thal diagoualises Vcrify vour choice:Lo DLhal p-'APmarksl2019 SemesterAssignmnentPage of ??(iii) Find te veelor A'5'7 IIINT: Writelinear CUnbinalion U FUUEcigcnvertors, thcn Use thc lincarity propcrty on A"(avt Ivz} . matk: A verlaill COLIQily in Aucklanl serviced by 3 superarkel slres A B & C. Assume the community population stable and that Cinstomer and do change to ditferent superm

Considcr thc matrix: Compute all eigcnvalucs andl thcir eigenvectors Vi MATk? Give Ilalrix F thal diagoualises Vcrify vour choice: Lo D Lhal p-'AP marksl 2019 Semester Assignmnent Page of ?? (iii) Find te veelor A' 5'7 IIINT: Write linear CUnbinalion U FUUE cigcnvertors, thcn Use thc lincarity propcrty on A"(avt Ivz} . matk: A verlaill COLIQily in Aucklanl serviced by 3 superarkel slres A B & C. Assume the community population stable and that Cinstomer and do change to ditferent supermarkets; February Ist study foutl that 1/4of thc Comuity shopped at store 1/3at store B; #nd 5/12 at store C. It Was also found that each month On aYerage store rcrained] 90% nf its customcr basc. but lost 10% to storc R_ Srore B reraincyl 5% of its cuslomuers bul lusl 85% u llem Wu slure ald 10% ol them slore C Slure relainexl 407 of its customcrs losing 50 tn storc and 10% to store B_ Wiite the transition matix P for this Markov PIOCCSS marks] Whal pruporlion O cuslOlers will each slure relain by Mareh Isl? [arks] I lle KAM pallern lomer dislribuliun cOnlinues wlal is (lle expecled Jong lert dislribuliuu o cusloqers amuwg lhe llree slores? [ark:l