# sol5 - (f(a T(o,0)=(1,0 \$010 T is not linear(5 T(cm cm 2...

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Unformatted text preview: (f (a) T(o,0)= (1,0) \$010) :% T is not linear (5) T (cm cm) 2 TLca, cal) = (ca. CZQIZ) CT(a,aL) = c (a. all) : (ca, caf) f” C”, I. T (“at M) # C (Tan (11)) => T 1‘5 not linear m T(%,0) +T(3Z[,0) = (13,03 +(;_L,o) : (13:qu D. T (gm) : (1,0) Tﬁffg 0) it T(§,a)+T(§.o) :9 T «‘5 no{' linear (d) T(I,0) + Tlv!,a) : u, 0) HM) :(2,0) T(o, o) : (0,0) Two) + THm) 1‘— T(0.0) T ,‘5 wk L‘nemr (3) TWO): (1,0) at (0.0) _-:> T :3 ml— (Mew 14.01). Suppose T is one—fwone‘ m A be a linearlg :ndefendezw 504.6565 2f V. 13‘ TM) is linearly defended. Hum ﬁlere exfsts V: Vnév. gun-ad]; W W a“ “=0, stcha/c a.T(v.)+~ Mam/“1:0 than TCQ'Vr+--~ + anVn) :0 Since T is one-b—ane, a.\/.+--'+aan:0 for not a“ 05:0 It Mfraoé‘ofs iv A is Gnarly indefendux‘, 5a TM) is linearly indefeadenﬁ “from T carries linearly indefme \$4st of V m» linearly indefwlmf “Bet a‘W. If T f5 not one-ﬁv—Me. {he/x A/CTHM. {we exis’cs \/.é\/, VHO 5qu #10126 cho)=0 SMCC {Va} is (£11er indefendw‘, {of is lineal/lg defaole/Lf, i6 ammo/rd; 50 T is media—one am/ mg! T carries linearfg z‘ndefendeaf what: of V orLJou (inwlg f/Lclefe/xdemf Subsets of W (L) SMIDPME 5 35 indefeILJe/vé, 57’ (a). US) is [illng :‘Ade’amg/mf 5.470055 T(5) ('5 [2‘11le faJeleJe/d. 13C 51‘s (I‘llng defendant 19m ﬂwre exv‘sts VI‘"VA65_ C(IV.+--- +aAvn;0. '9‘“ It]? Miraclt‘cts ~57 Tcg) ar"'a«6F Md nof ad 615:0 :ch wa “(TU/p) + ‘f’ anT(Vr\J-'30 “of a“ 0830 F5 (Marty I‘AJEPB/Lde/Uf 50 S is {:‘nwlg We}?de (c) Since (3 .‘5 {Mead} idefeaolenzt Hm. T(@) :‘5 «(50 [manly fade/Mnde Since T75 011-61. VIA/6W. EﬂéV Sun/L 7914f TLV1>LU. (>8me 6 is a Lasts 39? 1/, 191m: exfsfs a (~--4neF, 5f Vzalv,+---1-anyﬂ So 1»: NW a,Ttv.)+ fanT(Vn) e SfM T(€). 50 ﬂ?) is a bases for W, 17. (a3 romkm + nullity (T) : ohm (V) < Jim (W) :1) mkm < Jimmy) :5 RtTH‘W 50 T is not 07115:: (5) MAIN“ f MUFWU) : Jim (V) > elf/n (“U WANT) 5 00mm) => dimcw1+nuw'ty(n > elf/nu] => nwuv‘WTDO 50 T ,‘5 Me mesa—me 18. Tom): CM) NLT) : {(x,o) = MR 3_ Rm: {(7.0) wen; Zt7. Since V: is «Salas/we, 06%. 0:770) gT(l/,) Vw.,wzeT(V.)_ 3 12, vi eV, 56w,:T(1’.) WI: TM) Since V, (‘5 a Subsface V,+vzel/_ w.+W;= TMHM e TCl/r) VWIGTWI). 37/,eV, 5+, w.:T(v,), Since wev. 3‘me 66F, CIA/,2 CT(V,);T(cv,) e T(l/,) So TCVI) is a suL\$fﬂCe of W De/Loée V,=erV-' TmeW] Since T(o)=oeL{/, 06V VV, V161], “MTLVLHM T(zz,+vz):rw,)+nmew V.+Vze’17: vv‘er chnew. Tum: CTCVdeW, cv.eVi So IV; is 0L .sulemce of V. ...
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## This note was uploaded on 11/16/2009 for the course MAT 2030 taught by Professor Professorli during the Fall '08 term at Al Ahliyya Amman University.

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sol5 - (f(a T(o,0)=(1,0 \$010 T is not linear(5 T(cm cm 2...

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