Solved Problems on Linear Transformations - Review Sheet | MATH 215, Study notes of Linear Algebra

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@ Find a Jinear trans parma fion TY RY > R> st Tha apes onal - = Oo Tle kt] 6) Su pore that TR. = R” & a linear frons rma hion anol Suppose that v is a vector st Twitonbues tele (where thoe ToT) Prove. that vand Tv) are linvorly independent, @ Given te mahx A= = = A find a) chor. poly ao, =o 6 b) the eigenvalues c) a basis Sr cach ergenspre . WK = ae Find aj A o__@ bp A © Galuak the pllowing deferm'nen tS ; 2 eS eas | Jag tof @ 6 inca: : : b) sarees 2) A basis fr tee eigensp aces of A A dyaponali2a ble 2 Uf so, fird ar a “ ee" cade iP ja oe ee [4 { 2 | find! a) eipewalies of A ( d) Is javerh ble dhagonal. a Use the Coy Jey ~ Hamilton Sreorem (se CY characten'shc equation ) hk compuk Adi eon Tet AS be om Ged maky with eigenvalues S22 ee ergenspate js tro olimensronal , Can we onali'zqe? mahx sa hs res i pric fuiole Shot A tS hap j Ex plain : i alee ee matn'x a [' | Cas rh pook or 4a counkrexauple . 1@® Tre or false: Ep gi* a a)if an nxn matix A hos 2 jelent'ca | rows , Fen wet A= O b) If A is an nxn mahi x anol ronk(a)=n then akthA=-O. fae re a aise et Lee some x£0O