# m235Ass_3 - /t ZS 5/tr/ohhon n/ni t A-u!o-er 3 b 2/os 73,1...

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,//t ZS 5 A-u!o-er/ # 3 /os* 73,1* ,/tr/ohhon ,L rJf b a r,o/aloa aF-- ** t. n"/ni ftptoxah,b'; + ltv /2.). h.""4*,.t2'i T tA/u-< T: V rW an/ /t ; a ta; /*, V arr/ a- ; a l,a,; Jt* W. 6P ,41*-, tf Zft = ,ro. 'k aa"gr/ /rv"- (<a-or/tu>b ) moh-i /r*,, ,B /o-vlmob ,1 eo-dta|b "16/1" bt yl rz2urcy' -L- Q S Definition. Let L : V - V be a linear operator on a vector space V and let v € V. The L-cyclic subspace of V generated by t, ,S* is defined by sL,, Span({v, L(u), L'(r), . . ., rrft), . }) where fr\$) !-,o L o. .o L(u).

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,(r):: ({".*: ' _,c2, r (::): (r;:,;;,,,) (t)(?)) {(il ft) fi) } T: P2(R) - (a +2b+2c) {1, r, r2} 1. Find the matrix representations of the linear transformations below with respect to the given bases. (u) 7 : IR3 -' 1R3, o p ,rt., o :{ (i) fi) (i) } (ii) ,lTl, , "Y : (b) (.) T.C2 (i) Blr)P, P-{ ,trl,, ^t : { (l) (}) } T("*br+cr2) BlTlP, g : Pz(R), +(2a+b+2c)r* (2a*2b+")*' .,lTlr,J:{1 +r+12, 1-r,l-12}
Question 1 lr0 -r 2r + 3r2)lu and. T(L + 2r * 3r') and ? lrQ*2r-2*')1., and T(2 * - Z*'). to evaluate (i, L' (i) ], solutions to L'ft) l, 2. Use your (u) (i) (b) (i) (.) (i) (z r,\ \z+z) V(:;;)1, k(l :x)1 , (ii)

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Consider the linear transformations ? : IR2 - Pz(R) and S : P2(R) * Mz*r(R) given by T((o,b)') -(a+2b)+(-o 2b)r2, a3 s(p) - (#11,. .'r8l ) + 3b)r + (34 p(2) p'(L) p" (2) If Find (u) "lflB, (b) a[S]t, and find (.) ,[S o T)P two different ways. p-{ (l) ,(?) } 'Y_{r,*,*'}, ,:{(; s) (: ;)
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m235Ass_3 - /t ZS 5/tr/ohhon n/ni t A-u!o-er 3 b 2/os 73,1...

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