A Tutorial on Linear Algebra by Professor C. T. Abdallah

19 downloads 116824 Views 180KB Size Report
This chapter deals with the study of linear algebra and matrices as they are used in this course. ... We start this chapter by introducing matrices and their algebra.
        !#"%$ &')(+*-,.')/021436587239/;:+*-'1>'?3@*>1>A27?BC;DE:+(+F?39/5G/;:+H;36I25./J/;F)7KL/145.(M,N39*O/;*G1>'?36BL/5>3@A)*4397(+FL1>'2(+*G,NCPA25.*43;Q R SUT-VXW>TZY [=\^] _8`bacWedgfih>j@TGkaE_ l 3m*41>/5>1 1>'2(+*,.')/0214365nIoBp(+Fq145.Cr72A),6(+F?HsKL/145.(M,N39*n/;F27t1>'239(u5/;:+H;36I25./vQUw=C;1>/1>(+CPF2/;:+:uB;xyKL/145.(+,N39* /5>3m/ 5>39,N1>/;F?HPA):+/5X/5>5z/9BmC;D{39:u39K39Fo1>*X7239F?C;14397sIrBm,6/0)(u1>/;:G:+361414365.*J|X}>~}>€GQn&'?CP*43L39:+39K39Fq1>*X/5>35.36D365>5.397m14C /;**>,6/;:M/5.*‚/;F27m7?39F?C;14397sIoBƒ:uC„ŠG}.‹9ŒŽuQw@C;143L1>'2/1‚1>'?3L*.,6/;:+/5.*‚/5>3LF?C;1F239,N39*>*>/5.(+:+B ,NCPF2*41>/;Fo1>*6O1>'?36BK/9BrI‘3J5>39/;:EC;5=,NCPK0‡:u3N’ FrA2KXIb365.*6xv0bCP:uBrF2CPKL(+/;:+*6xrC;5=H;39F2365./;:ED“A2F2,N1>(uCPF2*9Q ”y•c–)—™˜›šœ^ž Ÿ8CPF2*>(M7?3651>'?3JKL/145z(¡’ ¤¥¥ §=¨  ¨P©;ª;«P¬ §@­;«  «v®„¬ §J®9¯  ¯;°P¬ §@­;©  ¨P° ¸.¹ ¥¥ ¨  ©;ªP¬L±s®6¨r²)³ §J®  ¯;°;°P¬ ¨  °;¯;­v®9© §´¬  ©;ª;«L±s®6¨r²2µ §=­ ¨  ©; ®„ª¬¨P¨P° ¯ §¶  °;«;§=ª¨ ±s ¬«;®6¨r©;ªP²)¬ · ¹¹¹ |£¢ ¥ ¨  ¨?®9©;­;­;¯ ®;®  ¬© §@©  «;­v®9« ¯  ¬ª;¯L±s®6¨ ²2µ §@­v®  «¨¶ ©;©  ­;°;« ¹ ¨ ® ¨ ¨ ¨ º ¦ ¨ ¨ ¨ ¨ ¨ ¨ §@­¨ &'2(M*(+*/ ª ’ « KL/145.(¡’ ' 5.39/;:E39Fq145z(u39*6QO»´Fn1>'23‚C;1>'?365@'2/;F)7Ex ¼½¿¾À ¢ÂÁ ¾‰ÄGà ¾{à ­ ¾8® à © ¾‰ÄGà ¾8à ª ¾­ à ¶mÅ (+*/ ©L±Æ© KL/145.(¡’ C;DÇ0bCP:uBrF2CPKL(+/;:+*8(+F 1>'?3È/5.(+/I‡:u3 ¾ Q É Ê LK /145.(u’Ë3‚ÕÇ¢ ® }6Ö6Ö6Ö.Ì×/;F27ÙØ!¢ ® }6Ö6Ö6ÖzÎZQ ”y•c–)—™˜›šœƒÚ&'?3!KL/145.(¡’Æ|U(+FÜÛZ’?/;K0):u3 ® '2/;* ª 5.C„'?3!39:u39K39Fo1@…)Ý4Ý¢ §=¨  ¨P©;ª;«P¬ árA2/5>3;QOÞâD›Ìߢ ® 1>'?3JKL/145z(¡’(+*/5>C‰< KL/145.(u’ ½ C;5@È;39,N14C;5 À Q{ÞâD›Îƒ¢ ® 1>'23JKL/145.(¡’n(+*/;FÆÌ×,NCP:+A2KLFÆKL/145.(¡’ ½ C;5=È;39,N14C;5 À Q{ގD›|ã(+*=*>áoA)/5>3‚1>'?39Fn'?3´å=æ;…o6‹JC;D›|çIrBÙ1>'23*>A2KèC;DÇ(u1>*72(M/H;CPF2/;:E39:u39K39Fo1>*6x)(éQê3;Q ½®À å=æ;…rN‹ ½ | À ¢ ìÑ+íÏë Ý …qÑ¡Ñ ®

”y•c–)—™˜›šœÜîçŸ8CPF2*>(M7?365 ¼½¿¾À C;D›Û-’v/;KL0):u3 ® 2x 1>'?39Fnå=æ;…o6‹ ½“¼Ù½¿¾À4À ¢ ¾„Ä-à « {¾ à ª Q É

Eï ðñï òèó‘ô;õqö¿÷çømùéúcû2üOõPó &339árA2/;:¿xE/;K3LFrA2KXIb365yC;D85>C‰}ñØ?Q&'2/1y'2/9È;3X1>'?3J*>/;K3XFoA2KXIb365.* C;DÇ5>C„A?I2145z/;,N1439739:u39K39Fo1IrBÙ39:+39K39Fq16x‡(¿Qê3;Q  ¢UÐ  ÑÓÒ Ô‘¢  ½© À |  þ   ÑÓÒ ¢ … ÑÓÒ ˆ ÑÓ Ò  Õ>}ñØ 1>'?3LK!A2:u1>(u0‡:+(+,6/1>(uCPFÆC;D © KL/145.(M,N39*|ÿ/;F27mþ 14CnC;I21>/;(+F  ¢ÿ|JÓþßKL/„BÜIb30b365>DC;5zK397Ë(uDG/;F27ËCPF2:+BÆ(uDO| '2/;*1>'23J*>/;K3FrA2KXI‘365=C;D›,NCP:+A)KLF2*/;*=þ '2/;*5>C„'?3KL/145z(¡’  (+*8Ì ± (uDÏ| (+*8Ì ± ÎË/;F)7þý(+*8Î ± Q-w@C;1431>'2/1þ|KL/„BF2C;136È;39FnIb3´723Nä‡F?397 /;F27 (u1 ,N365>1>/;(+F):uB(+*yF?C;1@39árA2/;:›14Cn|@þ 36È;39FËCv72A2,N1>*y/5>37?3Nä‡F2397EQ@&'23!KL/145z(¡’C;DG/;:+:6365>CP*‚(+*@1>'?3 wyA2:+:2KL/145z(¡’‘xr/;F27L1>'23@*>árA2/5>3yKL/145.(¡’L| 'مqÑ¡Ñc¢ ® /;F)7مoÑÓÒ@¢ ¨ DC;5OÕ ¢ Ø!(+*G1>'?3@(+7239Fq1>(u1âBLKL/145.(¡’bQÇ&'?3 (+7?39Fo1>(u1âBKL/145z(¡’ (M*7?39F?C;14397nIrB2Q-w@C;143J1>'2/1=| ¢q|£¢ |ã/;*>*>A2K(+F?H| (M*{Î ± Îs/;*=(+*)Q ïEð  õ û2õ;ôPöéû  ô"!-$û #&ó %'()Jòèó‘ô;õqö¿÷ ømùñúcû2üOõPó &'?3‚DCP:+:uC‰(u39*8C;DÇK/145.(¡’ Ê :uH;36I)5.//5>339/;*>(M:uBÈ;365.(uä)397 ® Q=| þU¢ *þ | © Q=| ã½ þ à  À ¢ ½ | à þ ÀEà  ­ Q=Š ½ | à þ À ¢àŠ›| à ŠÏþ DC;5=/;:+:E*>,6/;:M/5=ŠGQ ¶ Q=Š›|¢ |yŠ ª Q=| ½ þ  À ¢ ½ |yþ À  « Q=| ½ þ à  À ¢à|@þ à |  ¬ Q ½ þ à  À |¢àþ!| à  | ïEð + ,yõP.ó -/0)û 1 23-5476-úcó‘ô;û 1{.ó -/8 9ø 70;:?öéó‘ô;û ò ó‡ô;õq/;(+F?397 IrBÙ(MFq14365.,z'2/;F?HP(+F2H,NCP:MA2KLF2*8/;F27 5>C‰ ¢çXþ >†| >-Q@ÞeFÜ1>'?3!,6/;*>3!'?CP*43´C;DÏ|XQ e /145.(+,N39*=*./1>(+*4DBr(+F2H|£¢ | Y >™/5>g3 fgGSJWEFLhHKLNb7]/;F27 1>'?CP*43J*./1>(+*4DBr(+F2H|¢ § ?| Y >^/5>3 A\PQGVR;TNfgGSJWEFLhHKLNb7]2Q ©

Eï ðji kmû?ô;û2õmlàö3,NCPK0)/1>(uI‡:u3X/;F27ƒIbC;1>'Ë(+FoÈ;365>1>(uI):u3;Q´&'?365.3X/5>3C;1>'?365(+KL0‘C;5.1>/;Fq1 5>39:+/1>(+CPF2*(+FoÈ;CP:uÈr(MF?H(+FqÈ;365z*439*C;DZKL/145.(+,N39*9x2CPF?3‚C;DÇ'?3g¡•bQHKJWL£¢¤D]&¥QGSJDADLN[7](¦)GVEgEb ½ |Ý § | Ä | µ² Ý | · À ² Ý ¢ | ݲ Ý Ã | ² Ý | Ä ½ | µ § | · | ݲ Ý | Ä À ² Ý | · | ݲ Ý ½¶ À ”y•c–)—™˜›š'œ §›¨-5>C‰È;3 e Þ = É ¶

Eï ð© ªùéû5làû5-Ïô;óbõQ«|¬­û2õPó‘ôPö®)-…ó.-/8Uò ó‡ô;õqöC„< ½ C;5y,NCP:+A2KLF À IrBn/*>,6/;:+/5yŠ ­ Q C;e 1>'2A236:u1>5=(+0)5>:uC‰BÆ< /;½ FoC;BË5@5>,NC„CP< :+A)KL½ C;F 5XÀ ,NCP:+A2KF À IoBm/*.,6/;:+/5XŠ /;F27s/;7)7m1>'?3L5>39*.A2:u1>(+F?H 5>C‰< ½ C;5!,NCP:+A2KLF À 14Cƒ/;FqB w@C;143m1>'2/1Ù39/;,z'£C;D1>'?39*>3ƒ39:+39K39Fq1>/5.BtC;0b365./1>(uCPF2*KL/„BtIb3Æ5>360)5>39*439Fo14397 IoBt/™0bCP*41>K!A2:u1>(u0):M(+,6/1>(uCPFDC;5 ,NCP:+A2KFpC;0b365./1>(+CPF2* ½ C;5025>39K!A2:u1>(+0):+(+,6/1>(uCPF DC;5n5>C‰(uCPF2* À IrBt39:+39K39Fq1>/5.BàKL/145z(+,N39* 3 F?CPF2*.(+F?HPA2:+/5„Q ”y•c–)—™˜›šœ^ož ± = 361 ²³ © ® ¨ µ·¶ | ¢ ´ ¨ © ® ¸ ® ® §X® &'?39Fcx2:u361A2*43‚1>'?3JDCP:+:+C„C‰(uCPF)*6 ® Q=Û-’v,z'2/;F?H;3X5>C„(+0):uBL5>C‰< ® IrB s © /;F27n/;727(+114CL5>C„< ­ ­ Q e A2:u1>(+0):uBL5>C‰< © IrB _® ¹© /;F27/;727Æ(u114CL5>C‰< ­ ¶ Q e A2:u1>(+0):uBL5>C‰< © IrB _® ¹© ª Q e A2:u1>(+0):uBL5>C‰< ­ IrB "© ¹ª « Q e A2:u1>(+0):uB,NCP:+A)KLF ® IrUB s ® /;F)7/;727(u114CÙ,NCP:+A2KLF © ¬ Q e A2:u1>(+0):uB,NCP:+A)KLF ® IrB ® /;F)7/;727(u1{14C,NCP:+A2KLF ­ ¯ Q e A2:u1>(+0):uB,NCP:+A)KLF © IrUB s _® ¹© /;F27/;727(+114C,NCP:+A2KLF ­ &'?3‚39F)7n5>39*>A2:+1{(M* ²³ ® ¨ ¨ µ·¶ þU¢ ´ ¨ ® ¨ ¸ ¨ ¨ ® É

ª

”y•c–)—™˜›šœ^ž‡ž{‚(uÈ;39Fn1>'?3DCP:+:uC‰'?39Fn1>'23J,NC;5>5>39*40bCPF27)(+F?H!5>C„(+CPF2*/5>30b365>DC;5.K397c ® Q=(MFq14365.,z'2/;F?H;35.C„(+0):uBL5>C‰< ® IrB § ¾„Ä /;F27/;7)7(u114CL5>C‰< ­ ­ Q=K!A2:u1>(+0):uBL5>C‰< © IrB ¾{à ® /;F)7/;727n(u114CL5.C„< ­ Q &')(+*,NC;5>5>39*40bCPF27)*{14CL1>'?3‚DCP:+:uC„(u0):+(M,6/1>(uCPF2*OIoB 1>'?3KL/145z(+,N39*HP(uÈ;39Fc ®Q ²³ ® ¾{à ® µ·¶ ²³ ¨ ¨ ® µ·¶ ¼ Ý ½¿¾À ¢ ´ ¨ ¾‰Ä ¸ ¢ ´ ¨ ® ¨ ¸ ¼½¿¾À ¾Ä ¨ ® ¨ ¨ ©Q ²³ ® ¾{à ® µ ¶ ²³ ® ¨ ¨ µ ¶ ¼ Ä ½¿¾À ¢ ´ ¨ ¾ Ä ¸ ¢ ´ ¨ ® ¨ ¸ ¼ Ý ½¿¾À Ä ¾ ¿ ½ ¨ § ¾{à ® À § ¾Ä ¨ ¨ ­Q ²³ ® ¾{à ® µ ¶ ²³ ® ¨ ¨ µ ¶ ¼ · ½¿¾À ¢ ´ ¨ ¾ Ä ¸ ¢ ´ ¨ ® ¨ ¸ ¼½¿¾À ¨ ¨ ¨ ¾8à ® ¨ É

eÞ FH;39F?365z/;:¿x)DC;5@/;FoBKL/145.(¡’nC;DÇ5./;FЉ æ3972A2,N3X(u1Èv(+/L,NCP:+A2KFÆ/;F27n5.C„(uCPF2*14CÙCPF?3JC;D 1>'?3DCP:+:uC‰ ¼} ŸæÁ Sº ¨ ¨ ¨ËÅ w@3N’r16x‡,6A2*>*{È;39,N14C;5´*40)/;,N39*9Q «

½

¾pTn¿›`‘[@a.À _?ÁF V@T/¿›`‘[=aÄÃXÅ_¿ZTnÀ

ÞeFÆKCP*41=C;DZCPA?5=/020):M(+,6/1>(uCPF2*6x? Ä ä  Ü_Ñ b7]OՏG¼b"MVÖ @ ä ÐÒÑR…GÖob7¥QXG æ;Ý9 ½ æ Ä á@ À ¢ ½ æ;Ý>æ Ä À á@ ÎcJtGSA®°„Ï „Ý9 ½  Ä á@ À ¢ ½ ‰Ý. Ä À á@ ð"ϝì)[7JuG¼bMSÖ æ ä}ï ήJ¼GWAc°„è Ï  ä  ܇Ñb7]ÕG¼b"MVÖ~@ Ý }t@ Ä ä ÐÒ!Ñ æ‰ ½ @ Ý Ã @ Ä À ¢ æá@ Ý Ã æá@ Ä ÎcJtGSA®°„Ï  ½ †@ Ý Ã @ Ä À ¢£‰á†@ Ý Ã á@ Ä Ü ñ‡Ïì)[7J»b7¯¯5ASMDb7¯£bQJ\{A æ Ý }4æ Ä ä(ï ήJ¼GWAc°„{Ï  Ý }> Ä ä  Ü_Ñ;b7]ÕUG\b"MSÖò@ ä ÐÑR…GBÖÔb7¥7G ½ æ Ý Ã æ Ä À á@ ¢àæ Ý á@ à æ Ä á@ ÎcJtGSA®°„Ï ½ „Ý à  Ä À á@ ¢ ‰Ý9á@ à  Ä á@5Ü ómϝì)[7JFG\b"MSÖÒ@ ä ÐÑnR…GšÖob7¥7G ® á@ ¢ô@$R‘ÖÔGVJtGÒâ3LAšHhÖÔGX`Ô]&LKHKCL] ï ήJ¼GWA®°.ϝL]  Ï ”y•c–)—™˜›šœ^žvÚíç)֊GõV[7¯h¯£[7R;Lh]mab7J¼GÒ¯öLh]OG¼b7JÒ¥QG¼M_H®[7JFA®°ÔbMDGWAÒR;LKHhÖHh֊GUb0ADAS[IMILKb"HcG¼Õ(ASMDb7¯£bQJ?÷wGS¯Õ0AVÚ ï ë R;LKHhÖ ï Ñ  ë R;LKHhÖ  Ï É Æ mœ ǑÈÊɡÉhÌÈ ÚøÍAD`5ØWAIGVHc~ [ÙõòbÒ¥QG¼M_H®[7JA®°ÔbMDGÐÄLAòbFAD`5ØSA®°Ôb"MWGšL õ LhHnLèA»bÒ¯öL]OG\b7J»¥7G\MIH®[7JAc°Ôb"MWGòLh]­LKHhA»[QR;] JWL£aQÖmH®ÏFùƒ]OGX]OG\MDGWADASb7JWCM\[7]ÕQLhHKLN[7]ÒõV[7J=~ H®[Ø\GgbUAD`5ØSA®°Ôb"MWGgLAšHhÖobQHwLhHwM\[7]H®b7L]&AXHhÖÔG»ú_GVJÙ[¥QG¼M_H®[7JSÏ

”y•c–)—™˜›šœ^žrr’r’

Çðñï #=ö'?365./;(+7 14CIb3‚:+(+F239/5.:uB7?360b39F27239Fq16Q ë ë ”y•c–)—™˜›šœ^mž z &='?3*436Ò1 ‰‹6àÑ ’LÕ@¢ ® }6Ö6Ö6ք}4Î (+*‚:M(+F?39/5.:uBÜ(+F27?360b39F27?39Fo1´(+F ï ë QÙ»´FË1>'?3C;1>'?365J'2/;F27cxE1>'?3 © È;39,N14C;5.*6x@&>Ý ¢UÐ ®§^© Ô®ü@5>Ä ¢UÐ ©ã§s¶ ÔÏ/5.3J:+(+F?39/5z:uB7?360b39F27?39Fo1(+F ï Ä Q ¬

É @w C;143n1>'2/1/;FqB^*>361!C;D@È;39,N14C;5.*L,NCPFo1>/;(+F2(+F2HÜ1>'?36365>CËÈ;39,N14C;5(+*:+(MF?39/5.:uBm7?360b39F27?39Fo16Q Ê :+*>C?xG(uDI@ Ñ ’ ÕX¢ ®0b}639Ö6F2Ö67?ք39}4FoÎ16Q (+*yxÇ:+(+(+F)F2/;39/:+:u5.B;:uxbB(uDZ7?1>36'?0b339F2*47?361g39FoI16@)xbÑà/;’72(M72*@(+F?:+(MH F?39/ /5.F?:u36BnÝ´'?39'?C;3D-F?1>'?36< 3È;*43936,N1‚14C;:+(+5.F?*‚39/(+FÜ5z:uBn1>'?(+3F27?*4363S1 s KL/„BIb3‚(uCPFnC;DÇ1>'?3‚C;1>'2365.*6Q ý C„'?3Ì ± ÎK/145.(¡’ƒ|ÿ*‚,NCP:+A2KF2*6QXw@C;143L1>'2/1(+D Î ÿÌ 1>'?39Fƒ1>'?3*4361´C;DGÈ;39,N14C;5.*')/;*@14C Ib3:+(+F?39/5.:+B (MF27?360b39F27?39Fo16Q@&'2365>36DC;5.3;xb:+361yA2*´,NCPF2*.(+7?365y1>'?3,6/;*43 Ï|/;F27n,.'?39\, ‰(+D†(u1{(+*{F?CPF2*>(+F2HPA2:+/59xq(éQê3;Q-(uwD r  r¢  ¨ xv1>'?39F I@)àÑ ’J(+*=:+(+F?39/5.:+B(+F27?360b39F27239Fq16xrC;1>'?365>(+7?365›1>'?3{0):+/;F23 ï Ä /;F27*>A?020bCP*43 3´:+(+F?39/5.:+B!7?360b39F27239Fq16xo1>'?39UF @ Ä ¢ m… @cÝOC;58IbC;1>'LÈ;39,N14C;5.* :+(u3Ù/;:uCPF?Hƒ1>'?3*./;K37)(u5>39,N1>(uCPFEQÆÞâD1>'?36B^3 :+(+F239/5.:uBm(+F27?360b39F27239Fq16xÏ1>'?39F^1>'236BsDC;5zK 1>'?3 *>(+7?39*XC;D=/ 0)/5./;:M:u39:uC;H;5./;KnQÇ&'?365.36DC;5>3;xo(+F1>'?3=,6/;*43=C;Db:M(+F?39/5Z7?360b39F27?39F2,NB;xq1>'?30)/5./;:M:u39:uC;H;5./;KU7?36H;39F2365./143© 14CX/‚*.(+F?HP:u3 :+(+F23;Q l 3,6/;Fƒ39árA2(u0ƒ/È;39,N14C;5*40‡/;,N3X'ÆKL/;FoBD“A2F2,N1>(uCPF2*9Q@»´F?3JC;DG'?3X(MF2F?365=0)5>Cr7)A2,N17/ ‰;39*@1ñ,6/;:+/539(u1>'2365=(+F ï C;5=(+F  xv1>'?3C;1>'?365CPF23J(+*{1>'?3F?C;5zKèC;D›/È;39,N14C;5y7/ ‰;39*y/È;39,N14C;5y(M(F ÐU14C/L0‘CP*.(u1>(uÈ;3´È/;:MA?3(+F ï Q Çð   .ó cö û :r7ô †õ  {´(uÈ;39FÙ/È;39,N14C;5*40)/;,NB3 û^xo/9B1>'2/1 )Ñe}4ÕÇ¢ ® }6Ö6Ö6Ö.Ì ’@*40‡/;F û (uDb36È;365>BÈ;39,N14C;ƒ5 @ ä û KL/9BIb3(uCPFC;D ‡ÑŽx2(éQê3;Q ½« À @ ¢ ì  Ñ …q Ñ )Ñ DC;5{*>CPK3*>,6/;:+/5.*{…oÑâQ-&='?3‚*>,6/;:+/5.*{…oÑÏ/5>3´1>'?3‚,NCPK0bCPF?39Fo1>*{C;D @Æ(+FÙ1>'? 3 )ћ72(u5>39,N1>(+CPF2*6QZw=C;143‚1>')/1{F2C;1>'2(+F?H (+**>/;(M7/IbCPA? 1 )ћIb36B;CPF27n1>'?3D“/;,N11>'2/1=1>'?365>3(+*39F2CPA?HP'nC;DÇ1>'?39Kè14CK/;FoA?D“/;,N1>A?5>3‚36È;365.BnÈ;39,N14C;5y(+ F û™Q ”y•c–)—™˜›šœ^Ԟ — ­ È;39,N14C;5z*@(+F ï‚Ä É Ê *4361XC;DÈ;39,N14C;5.*3 Ñ }4Õ¢ ® }6Ö6Ö6Ö.Α’ (+F9û (+*X*>/;(+7s14CÜIb3/ÆI‡/;*>(+*‚C;Dû (uD(u1J*>0)/;F2*òû /;F27™(u1X(M*:+(+F?39/5z:uB (+F272360‘39F)7?39Fq16Q-&='2(+*(+*I)/;*>(+,6/;:+:+B1>'?3JK(+F2(+K!A2K FoA)KJIb365C;DÇÈ;39,N14C;5.*yF?36397?397Æ14CÙ*40)/;F­û^Q{&'?3J72(MK39F2*>(uCPF C;D‘ûÂ(+*1>'?3FoA)KJIb365C;DÇÈ;39,N14C;5.*y(+Fn/;FqBI)/;*>(M*C;Dû™QG&'rA2* ï ë '2/;*72(+KL39F2*>(uCPFÎZQ ”y•c–)—™˜›šœ^ož ™ = 36?1 û Ib3‚1>'?3È;39,N14C;5‚*40)/;,N3XC;DÇ/;:M:EÈ;39,N14C;5.* @n¢ÿÐ @ Ý Ö6Ö6ÖB@ ԍ>™*>A2,z'1>'2/1y/;:+:c,NCPK0bCPF?39Fo1>* /5>3´39árA2/;:¿QZ&'?393F û (+*8*40)/;F2F2397IrB1>'?3yÈ;39,N14C;5C;D†/;:M: ® *6QO&'?365>36DC;5>3´72(+K ë ½ û À ¢ ® QO»´F1>'?3@C;1>'2Ý 365'2/;F27Ex (u„D û (+*O1>'?3=È;39,N14C;5*40)/;,N3yC;Dc/;:+:)0‘CP:+BrF?CPK(+/;:+*ÇC;D†7?36H;5.363=Î §s® C;5{:u39*>*6xv/I)/;*.(+*G(+?*  ® }4Œz}4Œ Ä }6Ö6Ö6Ö9}4Œ ë ² ’@Cr7)A2,N1>*GC;DEÈ;39,N14C;5z*{'?39FDCP:M:uC„(uCPFCPF F?C;5.K*6Q ¯

Çð+ †‡-…--û2õÙõ";8/6/:rô"

Ê F(+F2F?365Ç025>Cv72A2,N1Z(+*Z/;FC;0b365./1>(+CPFIb361ñ,QÆ&'23DCP:+:uC„Cv72A2,N16Q Æ mœ ǑÈÊɡÉhÌÈàî Í ]•L]&]„GSJ °Jt[IÕ7`&MIHÕGN÷n]OG¼Õ[7¥QGSJb(¥7G¼M_H®[7JFA®°Šb"MDGFÐ LAÒbšõD`Ô]M_HKLK[Q]ýu}6) ÿ ÕmGK÷n]OG\ÕXõDJt[7E Ð H®[ R‘ÖÔGSJ¼G LèAXGVLhHhÖÔGVJ ï [7J  AD`&MSÖ­HhÖob"H  @†} ã } å } ä Ð âÏß@†} ã ÿy¢  ã Yt} @'ÿ R‘ÖÔGVJtGFHh֊G uY}6& ÿÄÕGS]["HcGWAXHhÖÔGFMD[7EB°¯jG¼¢­MD[7]I^W`QambQHcGIÏ ×oÏß@†} ãJ$à å ÿy¢  @†} ã ÿ à @Ï} å ÿ æmÏß@†}>Š ã ÿ´¢ Š @†} ã ÿ}  Š ä  ëÏß@†t} @˜ÿ ¨ R‘ÖŠGSJ¼GFHhÖÔG ¨ [IM\MI`oJDAg[7]5¯ÞCBõS[7J@n¢ "¨ é ”y•c–)—™˜›šœ^&ž œ &='?3A2*>A2/;:b7?C;1=025>Cv72A2,N1(+F ï ë (M*/;F(+F2F2365025>Cv72A2,N16Q É Çðji u cõl Ê ][QJDE (+*/ H;39F?365./;:+(9/1>(+CPFtC;DX1>'?3ƒ(M7?39/;*C;DJ72(+*41>/;F),N3ƒ/;F27 :u39F2H;1>'EQ Ê *n*41>/I)(M:+(u1ñB1>'?36C;5.Bp(+*A2*>A2/;:M:uB ,NCPF2,N365.F2397 '1>'23*>(6 3C;D´*4CPK3È;39,N14C;5z*Ù/;F27tKL/145.(+,N39*6x8*4Cv,6(+/14397Æ*.,6/;:+/5ä)39:+7 C;DÇ5>39/;:†FoA2KXIb365.* ï Q ڍz “ž œ "Ë_"Ì !#($Ì !—&%

l J3 *41>/5.1CPA?572(+*>,6A)*>*>(uCPFÙC;DÏF?C;5zKL*{IoBÙ5>36Èv(u36'?3KCP*>1D/;KL(M:+(+/5{F?C;5.K397n*40‡/;,N39*6x?1>'2/1(+*{1>'?3*>0)/;,N39* C;DZÈ;39,N14C;5.*y'Æ,NCPF2*41>/;Fo1@39Fo145.(u39*6Q{ÞeF1>'?3JDCP:+:+C„CP:+A?143È/;:+A?3C;D-… DC;5@/5>39/;:†… C;51>'?3XKL/HPF2(u1>A2723yC;DZ…(uDDžÙ(+*,NCPKL0):u3N’bQ Æ mœ ǑÈÊɡÉhÌÈZz|Íê][7JWE(') '[ÙõUb¥QG¼MIH®[QJ»@ôLAb­J¼G¼b7¯öTà¥0b7¯ö`5G¼ÕXõD`Ô]M_HKLK[Q]$ÕGN÷n]OG\Õ'[7]$HhÖÔGU¥7G\MIH®[7JFAc°Ôb"MWGXû AD`&MVÖHhÖÔbQH â*Ï '…+@ 'Iÿ ¨ õV[7JXb7¯h¯&@ ä û R;LhHhÖ,'/@' ¢ ¨ L õšb7]OÕ[7]&¯öCUL õ@n¢ ×o*Ï '8Š)&@ '*-prŠr.'/@+'ƒõS[QJXb7¯h¯5@ ä û b7]Õ b7]&CUASM\bQ¯£b7J´ŠƒÏ æm*Ï '…@ Ã~ã 'I/ Ž '/+@ ' à ' ã 'ƒõS[QJXb7¯h¯&@†} ã ä û$Ï ”y•c–)—™˜›šœ^žo   &='?3DCP:+:uC‰3Ÿ8CPKLKLCPF™F?C;5zKL*J(+F•û ¢ ï

' 5.39/;:c,NCPK0bCPF?39Fo1>*6Q ® Q ® sñF2C;5.Kn0 '/@'6Ý ¢ – uÑë íÏÝ r0@‡Ñ;r#Q

°

¨Ï ë œr— —^– ž ¦)GVH'@?'A@˜b7]OÕ+'»@B'ACØDGb7]&C(HKR/['][7JWEgA3[ÙõUb(¥7G¼M_H®[7Jò@ ä ï ë Ï~ç)ÖÔGS]$HhÖÔGSJ¼GG¼¢"LèASHhA÷n]&LKHcG °Ô[0AWLhHKLh¥7GM\[7]ŠASH®b7]5HhA Œ?FÝ b7]OÕҌ Ä AW`&MSÖ­HhÖobQH Œ Ý '/@' @ ŽD'n@+'ACXŽZŒ Ä 'n@' @› @ ä(ï ë &'231ñ'?3:u39KLK//5.3*>/;(+7Ë14CIb339árA2(uÈ/;:u39Fo1´/;F)7m1>'2(+*´0)/5.1>(+,6A2:+/5´025>C;0b365>1âBÜ'2/1 rr @‘rr Ý Ž G ­ rr @‘rr Ä rr @‘rr 7 Ž rr @‘rr%ø Ý Ž ­ rr @‘rr 7 rr @;rr Ä Ž G ­ rr @‘rr 7 ®6¨

É w@C;143L1>'2/1/nF?C;5.K K/9BƒI‘37?3Nä‘F?397m(+F27?360b39F27239Fq1>:uB D5>CPK×/;Fm(+F)F?365´025>Cv72A2,N16Q Ê :+*4C?x†'?3 H;39F?365./;:M(6397/;F?HP:u3‚Ib361â'?3(MF2F?365{025>Cv72A2,N16xv'?3‚C;5.1>'?C;H;CPF2/;:+(u1âBÙC;D © È;39,N14C;5.*@IrB ½¯ À @† ã ¢ @Ï} ã ÿ´¢ ¨ '2/M1 K!¢ ½ © Õ Ã ® OÀ NP © Q Q RÜ\W ÁT-_T a SUV_8`bW.B[ ÁFÀ ÞeFKL/;FoB,NCPFo145>CP:c0)5>C;I):u39KL*9xr/;F?36CPA2*:+(MF?39/5/;:uH;36I25./;(+,´39árA2/1>(uCPF)* …2Ý4¼Ý @†Ý à …2Ý Ä @ Ä Ã Ö6Ö6Ö Ã …)Ý @ ¢ ã Ý … Ä Ý¼@†Ý à … Ä4Ä @ Ä Ã Ö6Ö6Ö Ã … Ä ë @ ë ¢ ã Ä ë ë QQ ¢ QQ ½° À … ¼Ý @†Ý à … Ä @ Ä Ã Ö6Ö6Ö Ã … @ ¢ ã   ë ë  C;5=(+FnK/145.(¡’nF?C;1>/1>(uCPF ½ ®6¨ À B| @¢ ã DC;5@/;FÌ ± Î^KL/145.(u’n|Xx)/;FÆÎ ±s® È;39,N14C;5@Ë/;F27Æ/;FÆÌ×È;39,N14C;5 ã Q{&'?3‚0)5>C;I):u39K (M*14CLä‡F)7n1>'?3J*4CP:MA?1>(uCPF È;39,N14C;5 @†x?HP(uÈ;39FÜ| /;F27 ã QG&='?5>363‚,6/;*439*yKL(uHP'o11>7/ ‰;3J0):+/;,N3; ® Q=w@C*4CP:MA?1>(uCPF 3N’?(+*41 © Q Ê A2F)(+áoA23y*4CP:MA?1>(uCPF 3N’?(+*41>* ­ Q Ê F(+F?ä‡F2(u143´FoA)KJIb365C;DZ*4CP:+A?1>(+CPF2*{3N’v(M*41 ÞeFÙC;5z7?365{14CLA2F27?365.*>1>/;F27'?3´5./;F?H;3‚*40‡/;,N3/;F271>'?3‚FoA2:M:)*40)/;,N3‚C;D 1>'?3KL/145z(¡’|Xx?37?3Nä‡F?397 /;*DCP:+:uC‰*.(uI):u3‚:+(+F239/5=,NCPKJI‡(+F2/1>(uCPF2*=C;DZ1>'?3J,NCP:+A)KLF2*C;DZ|XQ@»´F 1>'?3LC;1>'2365J'2/;F27Ex†1>'?3FrA2:+:Ç*40)/;,N3LC;D{| 7?39F?C;1439Y7 X ½ | À Ä ¢ I@tbB| @ ¢ ¨ ’C;5X1>'?3L*4361C;D{È;39,N14C;5.X* @ ä ï ë *>A2,z'n1>'2/1=B| @ ¢ ¨ Q ”y•c–)—™˜›šœƒÚcž v '?C„ ')/Z1 W ½ | À (+*/L*.A?I)*40)/;,N3‚C;D ï  /;F)*7 X ½ | À (+*/*>A?I)*40‡/;,N3‚C;D ï ë Q É ®;®

w@C„'?3 :+(+F239/5X39árA2/1>(uCPF |@p¢ ã x-(u1X(M*JC;IrÈr(+CPA2*!1>'2/1 ã *>'?CPA2:+7^Ib3Ù(+F&W ½ | À DC;5/ *4CP:+A21>(uCP F @Æ14CL3N’?(+*416x‡(+F C;1>'?3651CPF?3X*>CP:+A?1>(uCPFEQOw=C‰(uCPFs14CÜB| @¢ ã xÏ1>'239•F @ ôà å (+*J/;:M*4CÆ/Æ*>CP:+A?1>(uCPFEQ&'?365>36DC;5>3;x›DC;5/ A2F2(MáoA?3*>CP:+A?1>(uCPFn14C3N’?(+*416x)'2/]1 X ½ | À ¢ Q&='2/1=39árA2(u5>31>')/1=1>'?3!,NCP:+A2KLF2*C;D-|ãDC;5.Kß/ I)/;*>(M*C;D;W ½ | À x‡(¿Qê3;QO1>'2/11>'?365>3J'?39K ¨ /;F271>'2/1=1>'?Ý 36B (uCPFÎZQ-&'?39Fcx?1>'?3|ãKL/145.(¡’ (+*(+FoÈ;365>1>(uI):+3´/;F) 7 @n¢ | ² ã (M*1>'?3A2F2(MáoA?3‚*4CP:MA?1>(uCPFEQ ^ SW>j@/T Á´V_Ah V/T Àç?_ ÁFÂ_SW>j@/T Á´VynT ¿›`‘[@.a À = 361´|ãIb3J/;FÜÎ ± Ì KL/145.(¡’bx‡/;F27Ü7?39F?C;143!1>'?3X,NC;5.5>39*40bCPF272(+F2HL(+7?39Fo1>(u1ñBKL/145z(¡’nIo­B )Q=&'?39FEx‘:u361 @‡ÑZIb3X/ F?CPFŠ6365.CLÈ;39,N14C;5y(MF ï ë /;F27a`2ÑÇI‘3*.,6/;:+/5=*>A2,z'n1>'2/1 ½ ®9© À B| @)Ñcb ¢ `&@)Ñ &'?39Fccx `2ц(+*8/;F39(uH;39FqÈ/;:+A?3yC;D†|/;F)U7 @‡Ñ†(+*O1>'?3y,NC;5.5>39*40bCPF272(+F2H39(uH;39FoÈ;39,N14C;59QO&'2365>3@'2339(+H;39FqÈ/;:+A?39*!C;D@| 36'?3 025>36Èv(uCPA2* 39árA2/1>(uCPF ½ | § `?KÑ  À @‡Ñ†¢ ¨ ½ ®9­ À w@C;1>(+F?HJ1>')//1 @ Ñ ,6/;FF?C;1OI‘3=1>'?3 6365>CXÈ;39,N14C;59x2/;F275>39,6/;:+:+(+F2H‚1>'?3@,NCPF27)(u1>(uCPF2*ZCPFÙ1>'?33N’?(+*41439F),N3@C;Dc*4CP:MA?1>(uCPF2* C;DZ:+(+F?39/5{39árA2/1>(uCPF2*9x23631>'2/1/;(+F/;FÎEeŒ dÙ7?36H;5>363@0bCP:uBrF2CPKL(+/;:¿x3;$x `2ÑZ(+*/;F39(+H;39FqÈ/;:+A?3‚C;DÇ|çC;D›/;:uH;36I)5./;(+,K!A2:u1>(u0‡:+(+,6(u1âBÌnÑâQ8»‚F?3‚,6/;F1>'?39F*.'?C„'239F*4C(+* `?Y юQ ý C„' © ,6/;*>39*6 ®9©

® Q Ê=& '?:+:Ç3939FE(uxvH;*>39A2Fo,6È,N/;39:+A?*>*>39(+*JÈ;39/:u5.BL3*>72A?(+I)*4*>1>1>(MF2(u1>,NA?161>´(+F?ގH‚Fm391>/;'),z(+' *‚39,6(u/;H;*4393;Fox›È½ |(+F?H!§ /;`5FqBÙÀ F?6'365>`™C,N/;CP*:+A2/nKL0)F/5.HP/;(uKLÈ;3936*{1436/;59:+:Q 39(+H;39FqÈ;39,N14C;5.*9Q ”y•c–)—™˜ÇšœËÚ)Ú = 361 ²³ ¨ ® ¨ µ·¶ | ¢ ´ ¨ ¨ ® ¸ §J®9¯ §@©P¬ §J®6¨ 1>'239FEx)*4CP:uÈ;3‚DC;5 r| § `5rê¢ § ` · §t®6¨ ` Ä §™©P¬ ` §t®9¯ ¢ ¨ (+F?H1>'?3J*.A?H;H;39*414397ÆKL361>'?Cr7 ²³ ` Ä Ã ®6¨ ` à ©P¬ ` à ®6¨ ® µ·¶ | qâØ ½ | § `& À ¢ ´ §X®9¯ ` Ä Ã ®6¨ ` ` ¸ ` §J®9¯ §@©P¬ ` §t®9¯ ` Ä *>CL1>'2/1DC;5 ` Ý ¢ §J® '2/1=,NCP:+A2KF ® (+* @cÝ8¢UÐ ®9¯ § ®9¯®9¯ Ô > v (+KL(+:+/5z:uB;"x @ Ä ¢UÐ ¬p§Ë©v®‚«;­ Ô > /;F)37 @ · ¢UÐ ®§ƒ«!­;« Ô > Q-&'?365.3y(+*8/;F?C;1>'?365KL361>'?Cr7ÙC;D†C;I)1>/;(+F2(+F?HX1>'?3 39(+H;39FqÈ;39,N14C;5.*yD5>CPKè1>'?3723Nä‡F2(u1>(uCPFIrB/;,N1>A)/;:+:uB *4CP:uÈv(+F?H| @‡Ñ†b¢ `?hÑ @)Ñ É @w C;1431>'2/1CPF),N3/;:+:‘39(uH;39FqÈ;39,N14C;5z*=/5>3‚C;I21>/;(MF?397Exv'?39K (+F /;F Î ± ÎËKCv72/;:EKL/145.(u’ ~ ¢ßÐ @cÝò@ Ö6Ö6Ö\@ ÔéQÙw=C;143Ù1>'2/11>'?339(uH;39FoÈ;39,N14C;5.*!/5>3F?C;1XA2F2(+árA?3*>(+F2,N3L(uD…@)Ñ(+*‚/;F^39(uH;39FqÈ;39,N14C;5„x 1>'239F*4C(+*/;Ä FoBnŠ)@‡ë ÑÇDC;5=/;FoBn*>,6/;:+/5=ŠOQ © Q F2v C;CP1-K3N3’v39(M*4(uH;16Q39Fov ÈA?/;02:+A20b39CP*Z*4M3 /5>`23Ñb5>(M36*-0b/;39FL/143939(u7EH;39†FoÞeÈF/;1>:+A?'23(+*Ç*4'3;xr/;/´FD/;A):u:+H;:o36*>I2365z1Z/;C;(+,D‘(+K!F)7?A236:u1>0b(u0)39F2:M(+7?,6(u391ñFoB‚1†Ìn39(uюH;QZ39Fo&È;'?3939,NFE14C;xq5.1>*G'?3@K72/9(MB!KC;395-F2KL*>(uCP/9BF C;D{1>'?3Ùw@A2:M:Z*40)/;,N3C;D| § `?KÑ Æ'23FoA)KJIb365C;D:+(+F239/5.:uBÆ(+F)7?360b39F27?39Fo1y39(+H;39FqÈ;39,N14C;5.* /;*.*4Cr,6(M/14397'a` Ñ (+*1>'?3‚H;36CPKL36145.(+,JK!A2:u1>(+0):+(+,6(u1âB Ñ C;D›1>'2339(uH;39FoÈ/;:+A23m` Ñ Q l 3X,6/;FÜ72(+*41>(MF?HPA2(+*>' ­ ,6/;*>39* ½ / À x)A2:+:uB^7236H;39F?365./143,6/;*43 т¢ ÌnÑâގF 1>'2(M*X,6/;*43n1>'2365>3 (uCPF2*X14C ½ | § ` Ñ  À @ Ñ 5./1>'23651>'2/;gF d>A2*41CPF?3;Q ”y•c–)—™˜ÇšœËÚ2| î {´(uÈ;39Fn1>'23JKL/145.(¡’ ¤¥¥ ®6¨ P ­ ® §J® §J® P ­ ¸.¹¹ |¢ ¥ §@© ¨ P ­ ¶ ® ¨­ §J®¨ P ­ ¹ ¦ §@© P ­ ® §J® ®;® P ­ º ®9­

&='?39FEx2(u1>*,z'2/5./;,N14365.(M*41>(+,‚39árA2/1>(uCPF(M* f ½` À n ¢ ` µ §t®N¶ ` · à ¬© ` Ä § ®9«¨ ` à ®9©;¯ ¢ ¨ &='?365>3L/5>3 5>CrC;1>*6 Q-· &'?39FEx?µ '?39F *4C (M*Ù/;FoB ã ¢ – Ñ+ íÏÝ Š†KÑ @)юQ  ½ I À v (+K0):u37?36H;39F2365./143@,6/;*43 Ñc¢ ®  ý 365>3='23ä)5.*41Z39(+H;39FqÈ;39,N14C;5(+F1>'?3@A2*>A2/;:2KL39/;F2*6x 1>'239Fn3C;I)1>/;(+F?397/;* B| @ Ý ¢ ` Ñ @ Ý ½ | § `?Ñ À @ Ä ¢ @cÝ QQ ¢ QQ ½ | § `?Ñ À @ ¢ @ ² Ý ½ ®„¬ À w@C;143J1>')/1=/;:+„: @)ÑÇDCPA2F27 1>'2(M*{*,.'2/5z/;,N14365.(+*41>(+,0‘CP:+BrF?CPK(+/;:b(+* f ½` À b ¢ ` µ à ¬ ` · à ®9¯ ` Ä Ã ©¨ ` à ¯ ¢ ¨ 1>'239FE x ` Ý ¢ §X® x ` Ä t ¢ ` t ¢ ` ¢ QU&'?3ƒ39(uH;39FoÈ;39,N14C;5C;D ` Ý (M*39/;*>(M:uB DCPA2F27p14C Ib3 @†Ý¢ÂÐ §J®ƒ® §®ƒ® Ô > Qm»´F^· 1>'23ÙC;µ 1>'?365§@'2/;© F27cx›CPF23Ù39(uH;39FoÈ;39,N14C;5 ¨ D §y© (+*XDCPA)F27s14CËIbU3 @ Ä ¢ Џ   Ô >Gxb1>'?39'F @ ¢ ½ | à  À @ :u39/;72(+F?H14C @ ¢ Ð    Ô > /;¨ :M*4®9C?©;&x ª @ · §™¢ ¨ ½ ©;| ªà ¨ © ªJ §pÀ @ ®µ *>C1>'2/?1 @ µÄ ¢ Ð ¨  ®9¯P¬©ª §^· ¨  ®9¯P¬ªÙ¨  ®9©;ªL¨ · Ô > ¨ ®9¯P¬ª §™¨ ©;ª¨ ©;ª¨ É ®N¶

½ , À ´{ 39F?365./;:Z,6/;*43 ® Ž Ñ ŽÌ Ñ  ý *>CP:uÈ;31>'?30)5>C;I):u39KýIrB(+F?H ½ | § `?KÑ  À @†Ý ¢ ½| § ` Ñ À@ Ä ¢ ½ | § `?KÑ  À @ · ¢

365>3;x†/H;39F?365./;:Ç14C;0&sñ7?C„'?Cr7Ë*>'2CPA2:+7ÜI‘3A2*4397cQ ý 365>3(+FrA?39*A2Fo1>(+:Ç39/;,z's1>'?3(MF27?3N’Œ Ñ C;MD ` Ñ QÙ&'2(+*‚(+F)7?3N’ƒ(+*´DCPA2F27m/;*J1>'?3 *.KL/;:+:u39*41(MFq1436H;365y*>A2,.'1>'2/1 ½ ®9° À æ;…q)Î Œ ½ | § `2hÑ  À ¢ Î § ÌnÑ 1>'23y(+F)7?3N’(MF272(+,6/1439*G1>'?3y:+39F?H;1>'LC;Dc1>'23@:uCPF?H;39*>1O,.')/;(+FC;DE39(+H;39FqÈ;39,N14C;5.*/;F)7H;39F?365z/;:+( 6397Ù39(uH;39ÔF s È;39,N14C;5z*@/;*>*>Cr,6(+/14397Æa' `2ÑâQ ”y•c–)—™˜ÇšœË5Ú — ¤¥¥ ¨ ¨ ® ¨ ¸ ¹¹ |¢ ¥ ¨¨ ¨¨ ¨¨ ¨® ¹ ¦ ¨ ¨ ¨ ¨ º (+1>*,.'2/5z/;,N14365.(+*41>(+,0‘CP:+BrF?CPK(+/;:b(+* f ½` À b ¢ `µ ¢ ¨ *>C `bÝO¢ ¨ 'ÌËÝO¢ ¶ QZw=3N’v16xrDC;5.KU| § `E¼Ý !¢ |Xxo/;F27723614365.KL(+F?31>')/1Zæ…o)Î Œ ½ | § `b¼Ý  À ¢ © Q &='?365>3/5>31>'?39F © 39(+H;39FqÈ;39,N14C;5.*J/;F27 © H;39F2365./;:+( 6397ƒ39(uH;39FoÈ;39,N14C;5.*6Q!&'?3XárA?39*41>(+CPFƒ(M*@' ©(MF2Qn7?3N&ϒmCÜ(+,z*š'?Œv39¼,ÝX‰s¢ 1>')/Q16xÇ1>'2F2(+C;*1431>'?1>39'2Fs/1XHPA2Î /5z§ /;FqÌ 143639¢ *X¨1>'2xZ//;1JF2CP7sF21>3'2/,.'21J/;æ;(MF^…o)Î '2Œ /;½ *| :+39§ F?H;` 1>Ý '  À Ä xÇ¢ KL/7¨ ‰vx›(+1>F?'?Hn365>1>36'?D3C;5>:u3;39xÇF?H;1>'?1>' 3 C;DZ1>'23JC;1>'?365´,.'2© /;(MF © ?Q xÇ(u5.*416x‘,NCPF2*>(+72365 ½ | § `E¼Ý  À Ä @Æ¢ ¨ Ê FoBnÈ;39,N14C;5‚*>© /1>(+*eä‡39*=1>'2(M*39áoA)/1>(uCPF I‡A?1´CPF2:uB ¶ È;39,N14C;5z*J/5>3L:+(MF?39/5.:uB(+F)7?360b39F27?39Fo16Q = 361A2*‚,z'?CrCP*43Ò@cÝ¢ Ð ®¨n¨n¨ Ô > Q!ގ*1>'2(+*´/;F 39(+H;39FqÈ;39,N14C;5ÙC;5/ƒH;39F?365z/;:+( 6397 39(uH;39FoÈ;39,N14C;W5 þ Þâ1(+*!/;F39(uH;39FoÈ;39,N14C;5*>(+F2,N3 ½ | § `E\Ý  À @cÝ¢ ¨ Q v (+KL(+:+/5z:uB;x;@ Ä ¢ÍÐ ¨ ®n¨m¨ ԍ> (+*/;F39(+H;39FqÈ;39,N14C;59Q »´F1>'?3nC;1>'?365Ù'2/;F27Exn@ · ¢ Ð ¨^¨®n¨ ԍ> (+* /ÆH;39F?365./;:+j( 6397^39(uH;39FoÈ;39,N14C;5*>(+F2,N3 ½ | § `2NÑ  À @ · Ä ¢ @c­Ý ¢  ¨ Q v (+KL(+:+/5z:uB;.x @ µ ¢×Ð ¨Æ¨Æ¨™® Ô > (M*J/ H;39F2365./;:+(6397n39(+H;39FqÈ;39,N14C;5‚/;*>*4Cv,6(+/14397Æ' @ Ä Q É

ÞeFƒ*>A2KLKL/5.B39/;,z'ËÎ ± Î KL/145.(¡’Æ')/;*=Ι39(uH;39FqÈ/;:+A?39*y/;F27ÜΙ:+(MF?39/5.:uB (+F27?360b39F27239Fq1È;39,N14C;5.*9x‘39(+1>'?365 39(+H;39FqÈ;39,N14C;5.*yC;5H;39F2365./;:+(6397n39(+H;39FqÈ;39,N14C;5.*9Q ®9ª

i-ðñï uÊcõ8-ó.-Tv;†õl

w /;*4397CPF1>'?3n/;F2/;:uBv*>(+*!/IbC„È;3;x8'?3Yx;C;5z72/;F DC;5.K C;D@/;FqB ΠΣKL/145.(¡’bQmÞeF™D“/;,N16xO(+D '2/± 1L|B@)ÑJ¢{`2Ý Ñ@‡ÑŽxG1>'?39F:u361 ~ ¢UÐ @c?Ý @ Ä Ö6Ö6BÖ @ Ôéx2/;F2Y7 |¢ qPÕñj… } ½ `2Ñ À QG&'2(M*8:+39/;72*{14C|y~ Ý ¢£~~|@Q l 3ò‰vF?C„'2/1~ ² 3N’?(+*41>*=*>(+F2,N3 /;:+:G39(uH;39FqÈ;39,N14C;5z*L/5>ë 3Ù(MF27?360b39F27?39Fo1J/;F27^1>'?365>36DC;5>3|ÿ¢ ~ |@~iQÜ&'23Ix;C;5.7)/;F^DC;5.KÂC;D=|è(+*X1>'?39F&|@Q ގD-1>'?339(uH;39FoÈ;39,N14C;5.*J/5>3C;5>1>'2CPF?C;5.KL/;:¿xE~ ² Ý ¢U~ > Q‚ÞŽFƒ1>'?² 3,6/;*431>')/1 Ñ-¢ãÌnÑâxECv,N36397Ë1>'?3*>/;K3 /;(+F €t ¢ |=QÙ»´Fs1>'?3C;1>'?365J'2/;F)7Ex†(uD Ñ8¢ x†1>'?39FsA)*>(+F?H 1>'?339(uH;39FoÈ;39,N14C;5.*!/;F27ËH;39F?365./;:M( 6397 39(uH;39FoÈ;39,N14C;5.*/;*,NCP:+A)KLF2*OC;D†~ '?39F ²³ ®  ¯ ¨  ° ® µ¶ ¨ Ý ~ ² ¢ ´ §J® §J®  ®9«P¬ §=¨  ®9«P¬ ¸ ¨  © ¨  ©;«;«P¬ ¨  ¨P«P¬ 1>'?39YF |¢ ~ ² Ý |@~iQ É

®9«

”y•c–)—™˜›šœƒÚ„œ*{‚(uÈ;39Fn1>'?3JK/145.(¡’

¤¥¥ 6® ¨ P ­ ® §J® §X® P ­ ¸ ¹¹ |£¢ ¥ §@© ¨ P ­ ¶ ® ¨­ §X®¨ P ­ ¹ ¦ §@© P ­ ® §J® ®;® P ­ º &'?39Fcx2(u1>*,.'2/5z/;,N14365.(+*41>(+,39áoA2/1>(+CPFÆ(+* f ½` À b ¢ ` µ §p®N¶ ` · à ¬© ` Ä §t®9«¨ ` à ®9©;¯ ¢ ¨ &'?365.3/5.3 5>CrC;1>*6x…` Ý ¢ x` † ¢ `  ¢ ` ¢ Q l 3L,6/;Fƒä‡F27ƒ1>'?339(uH;39FoÈ;39,N14C;5X/;*>*4Cv,6(+/14397m',` Ý /;* @cÝ8¢ Ð §J®‚¨U¶ §t®£§p® Ô > Q-&© '?39FEÄ x? ü@ · Ð ¨Æ®L®‚¨ Ô > ü?@ Ä ¢ Ð ¨®¨­ Ô > &='?365>36DC;5>3;x ¤¥¥ §J® ® ¨ ¨ ¸.¹¹ ~ ¢ ¥ §J¨ ® ¨¨ ®® ¨® ¹ ¦ §J® §@© ¨ ­ º 1>'?39F ¤¥¥ §J® P ­ ® P © §J® P © §J® P « ¸.¹¹ ~ ² Ý ¢ ¥ §J® ® P P « ­ ®® PP ©© §J® ® P P © © §J§J®® PP «« ¹ ¦ ® P ­ ® P © §J® P © ® P « º 1>'?39F ¤¥¥ © ¨ ¨ ¨ ¸ ¹¹ ¥ ¹ €ƒ¢ ¨ ¶ ¨ ¨ ¦ ¨¨ ¨¨ ¶¨ ¶¨ º É ”y•c–)—™˜›šœƒÚ5 w@C„(+72365

¤¥¥ ¨ ® | ¢ ¥ ¨¨ ¨¨ ¦ ¯ §@©¨

¨ .¸ ¹¹¹ ® ¨ ¨ ® º §J®9¯ §´¬ ¨

(u1>*,z'2/5./;,N14365.(M*41>(+,‚0bCP:uBvF?CPKL(+/;:b(+* f ½ ` À ¢b` µ à ¬ ` · à ®9¯ ` Ä Ã ©¨ ` à ¯ ¢ ¨ ®„¬

1>'?39FEx$` Ý ¢ §J® x` Ä b¢ ` · b¢ ` µ ¢ @§ © Q/xÇ(+F2739(uH;39FoÈ;39,N14C;5.*´/;*Ib36DC;5>3/;F27nDC;5.K ¥¤¥ J§ ® ® P ¯ ¨  ®9¯P¬ª ¨  ®9¯P¬ª ¸ ¹¹ ~ ¢ ¥ §J® ® §X® ®P P © ¶ §J® ® P P ¶ ¶ §@¨ ®  P ®9¯¯P¬ª ¹ ¦ ® §X® ¨ ¨ º &'?39Fcx ¤¥¥ §J® ¨ ¨ ¨ ¸ ¹¹ ¥ ¨ §@© ® ¨ ¹ €Ü¢ ¦ ¨¨ ¨¨ §@¨ © §@® © º ”y•c–)—™˜›šœƒÚ5§

(u1>*,z'2/5./;,N14365.(M*41>(+,‚0bCP:uBvF?CPKL(+/;:b(+* *4C`EÝO¢ ¨ =< (+1>' ÌËÝ8¢ ¶ QG&'?39Fcx 1>'?365>36DC;5>3JK/7‰r(+F2H

¤¥¥ ¨ ¨  | ¢ ¥ ¨¨ ¨¨ ¦ ¨ ¨

® ¨ ¸.¹¹¹ ¨ ® ¨ ¨ º ¨ ¨

f ½ ` À ¢n`

¤¥¥ ® ~ ¢ ¥ ¨¨ ¦ ¨

É

µ¢ ¨

¨ ¨ ¨ ® ® ¨ ¨ ¨

¤¥¥ ¨ ® ƒ€ ¢ ¥ ¨¨ ¨¨ ¦ ¨ ¨

¨

¸ ¹¹

¨ ¹ ¨ º ®

¨ ¨ ¸.¹¹¹ ¨ ¨ ¨ ® º ¨ ¨

®9¯

É

zW he`‘[ Á ˆ?‰T-[@aETŽ w@C;143J1>'2/1=| Ñ ¢ |^Ö6Ö6Ö | (c1>(+K39*6Q-&'239FEx?'?36C;5.39K ‘†œoÌ"!œr— ž = 361=| I‘3/;FÎ ± ÎsKL/145.(¡’'n/L,z'2/5./;,N14365.(M*41>(+,‚39árA2/1>(uCPF r ½ | § `5 À ¢ f ½ ` À ¢ ½ § ` À ë à  ² Ý8` ë ² Ý Ã Ö6Ö6Ö Ã ‰Ý8` à  g ë ¢ ¨ &'?39Fcx f ½ | À ¢ ½ §J® À ë | ë à  Ý>| ë ² Ý Ã Ö6Ö6Ö Ã ‰Ý.| à  g  ë² ¢ ¨ ‡

ˆ?‰T/Š _T)‹ Œ è_ZŽ

”y•c–)—™˜›šœÜî±nLy*43‚1>'?3Ÿ{/9Bv:u36Bms ý /;KL(M:u14CPFn1>'?36C;5>39K 14Cä‡F27 1>'23(+FqÈ;365z*43C;DÇ/LKL/145.(¡’n| ¨ ¢ ½ §J® À ë | ë à  ë ² Ý.| ë ² Ý Ã Ö6Ö6Ö Ã „Ý.| à  g  1>'?39FEx ¨ ¢ ½ §J® À ë | ë ² Ý Ã  ë ² Ý.| ë ² Ä Ã Ö6Ö6Ö Ã ‰Ý\ à  g | ² Ý | ² Ý ¢  ® g Ð ½ §J® À ë | ë à  ² Ý.| ë ² Ý Ã Ö6Ö6Ö Ã ‰\Ý ;Ô ë

½ ©¨ À ½ ©v® À

É

] [=aET [BÁ ] _8`bacW¼¿ZTnÀ &'?3y3N’v025>39*>*>(+CPFY ã }>|@˜ÿy¢ ã >†|B@(+*O/XI)(+:M(+F?39/5GDC;5.KnQ l '?39F ã ¢@nA)KUC;DE/J*4BvKLK36145.(M,/;F27L*t‰;3639/;:¿x /;F27 C;DÇ/ ý 365zKL(u1>(+/;Fn/;F27n*¼‰;36(+/;Fn(uD›(u1(+*,NCPK0):+3N’‘Q-&'239FnF?C;1431>'2/10@Ï}>|@˜ÿy¢ @Ï}>|“¼@'ÿ(+D |ç(+*5>39/;:¿x2/;F)q7 @†}>B| @˜ÿy¢  @†}> | ”@(ÿ(uD›|ã(+*,NCPK0):u3N’bQ ©Çðñï F)ö¿ôPNö ˆÏ:û •Skm—û –w-Göéô;û^òèó‘ô;õqcö :v5û  {´(uÈ;39FÆ/;FÎ ± ÎsKL/145.(uY’ ˜x?1>'?39F ® Q ˜ (+*0bCP*>(u1>(+È;S3 sñ7?3Nä‡F2(u143;x?(uD›/;F27nCPF2:+BÙ(u]D @†8} ˜»@(ÿ ÿ ¨ DC;5@/;:+„: @•¢  ¨ Q © Q ˜ (+*0bCP*>(u1>(+È;3´*>39KL(+7?3Nä‡F)(u143‚(uD @Ï8} ˜@'ÿ ¨ DC;5=/;:+„: @ÏQ ®9° ’

­ Q˜ (+*(+F)7?3Nä‡F2(u143´(usD @†8} ˜»@'ÿ ÿ ¨ DC;5=*>CPK3ò@Ü/;F)7q@†}8˜»@'ÿ ¨ DC;5=C;1>'?365@ÏQ ˜£(M*ZF?36HP/1>(uÈ;3@723Nä‡F2(u143 ½ C;5G*439K(+7?3Nä‡F2(+143 À (+D § ˜ (M*Z0bCP*>(u1>(uÈ;37?3Nä‡F)(u143 ½ C;5G*439KL(+723Nä‡F2(u143 À Q›ÞâDl˜£(+*G*4BrKK36145.(+, 1>'?39F/;:M:E(u1>*39(uH;39FoÈ/;:MA?39*/5>35.39/;:¿Q ”y•c–)—™˜›šœÜ ’r’r’ É ™

šœ› ž'?3!È;39,N14C;5.*‚(+*y/ :+(+F239/5,NCPKJI)(MF2/1>(uCPF C;DÇ1>'?3C;1>'?365=È;39,N14C;5.*@(MF 1>'?3J*43616Q ¤ !0Ì"¥Çšœr— î v '?C„'2/1@/;FqBn:+(+F239/5,NCPKJI)(MF2/1>(uCPFnC;D›È;39,N14C;5.*@D5>CP„ K ¦p(+*/;:M*4C(+§F ¦@Q ¤ !0Ì"¥Çšœr— z Ê 5>3‚1>'?3JÈ;39,N14C;5.*=(+F 1>'23I)/;*>(+*{DC;5=/0‡/5>1>(+,6A2:+/5*.A?I)*40)/;,N3A)F2(+árA?‡3 þ ¤ !0Ì"¥Çšœr— —ø{‚(uÈ;39Fs/I‡/;*>(+*‚DC;5J/Æ*.A?I)*40)/;,N*3 ¦@xÇ,6/;Fs36È;365>BmÈ;39,N14C;5(++ F ¦çIb3LA2F2(+árA?39:uBÆ5>36025>39*439Fo14397^/;*!/ :+(+F239/5,NCPKJI)(MF2/1>(uCPF C;DÇ1>'?39*43I‡/;*>(+*{È;39,N14C;5.D* þ ¤ !0Ì"¥Çšœr— ™ v '?C„'2/1@(uDÏ|ç(+*/L*4BvKLK36145z(+,´KL/145.(¡’ ½ (¿Qê3;Qux2|¢ | >-x?,N5.(u0)1Gå 7239F?C;1439* 145./;F2*>0‘CP*>3 À x?1>'?39F @ > | ã ¢ ã > | @ DC;5=/;:+:bÈ;39,N14C;5.B* @ƒ/;F)7 ã C;DÇ1>'?3J/0)025>C;025.(M/143´7)(+K39F2*>(+CPFEQ {´(uÈ;39F ¨ ½ @ À ¢ ® @ > B| @ à ˆ > @ à Š 5>7?3936*40b0b39CPF2F2727239(MFqF?D1 Hþa39xP(uH;A239*4Fq1>È;(+D39BÙ,N14B;C;CP5zA?*@5=C;/;DZF21>*4')'?3J39(+H;39FqÈ;39,N14C;5.* ­ MQ Ly*431>'23!Ÿ{/9Bv:u36mB s ý /;K(+:u14CPFn1>'?36C;5.39Kè14CLä‡F)7Ù1>'23J(+FoÈ;365.*43‚C;DZ| ½ (+D›|ç(+*(+FoÈ;365>1>(uI‡:u3 À Q ¤ !0Ì"¥Çšœr—  çŸ{CPF2*>(+7?365{1>'?3X*>/;K3KL/145.(u’ ²³ ® © ­ µ ¶ |¢ ´ ¨ © ­ ¸ ¨ ¨ ¶ ® QÞe*1>'2(M*KL/145.(¡’0bCP*>(u1>(uÈ;S3 sñ7?3Nä‘F2(u14‡3 þnF236HP/1>(uÈ;S3 sñ7?3Nä‡F2(+14‡3 þÆ(MF27?3Nä‡F2(+14‡3 þ§xPA2*>1>(uDBB;CPA?5@/;F2*>39Fo1KL/145.(+,N39*='2/9È;3X1>'?3*>/;K339(+H;39FqÈ/;:+A?39D* þ­xPA)*41>(uDBB;CPA?5=/;F)*4C„È;3J1>'?3025>36Èv(uCPA2*{5.39:+/1>(uCPFEx2A2*>3(u114Cä‡F27‹ ‹"³ (+D | ¢ Á ¨® ©®nÅ ¤ !0Ì"¥Çšœr— mž ± = 361L| I‘3n/ËKL/145.(u’™D5>CPK ï ë 14C ï  (¿Qê3;Q| '2/;*Ìg5>C‰'2/1L(+D @ ä'ï ë x?1>'?39F ã ¢ |B@ ä'ï  Q ©v®

® Q *.v A?'?I)C„*4,N'23‚/1{C;D 1>'?ï 3‚wyQ A2:+:‘*40)/;,N3´C;DÏ|XxµX ½ | À (+*{/*>A?I)*>0)/;,N3@C;D ï ë /;F271>'2/11>'?3´5./;F?H;3´C;D›|Jx:W ½ | À (+*{/  ý 39F2,N3;xcX ½ | À /;F)7aW ½ | À '2/9È;3(uCPF2*9Q8ÞeFÜD/;,N16xb1>'?3!72(+K39F2*.(uCPFnC;D'23J5./;FЉ C;DG| 7239F?C;14397ƒIoBæ;…oÎ)Œ ½ | À '23!FrA2KXI‘365yC;DG:+(MF?39/5.:uBn(+F27236‹¼0‘» 39F)7?39Fq1,NCP:MA2KLF2*y(+Fƒ|JQ ¶y39F?C;1431>'?3 72(+KL39F2*>(uCPF C;DlX ½ | À IoB ÎJ· ½ | À Q{&'?39FÜ,NCPF2*>(+72365=/;FqB I)/;*.(+*I@)Ñà’ Ñ+ëíϸº¹ Ý C;DlX ½ | À x‘/;F)7,NCPK0):u36143X1>'2(+*I‡/;*>(+* (+Fo14C/LI‡/;*>(+*C;D ï ë IoBn/;7272(MF?HÎ § JÎ · ½ | À :+(+F?39/5.:+BÙ(+F272360‘39F)7?39Fq1{È;39,N14C;5.X* I@ Ñ ’ Ñ+ë í ‹»èyÏÝ Q{&'?365.36DC;5>3;x‘/;FqB @ ä'ï ë KL/„BIb3‚(uCPFnC;‘D @‡Ñ›*4C1>'2/1 ë ¸º¹ @ ¢ ìÑ+íÏë Ý Š†hÑ @)Ñ ® Q w:M(+F?B39/DC;5.:u5.BÙKL(+(+F2F27?HË360bB| 39@£F27?*>39'?FoC‰16< QZ&1>'2'?/3615>361>DC;'25>33;x2È;*>39'2,N14C„C;3 ë ¸º¹ ½ë ¸¾¹ æ…o)Î Œ ½ | Àcà JÎ · ½ | À ¢ Î ¤ !0Ì"¥Çšœr— ž)ž v A?020bCP*43 @ (M*O/XÈ;39,N14C;5(+F X ½ | À Q v '?C‰'2/w1 @n(+*OC;5>1>'?C;H;CPF2/;:‘14C!36È;365>BLÈ;39,N14C;5=(+²F W ½ | > À Q ¤ !0Ì"¥Çšœr— žrÚ {´(uÈ;39F/m*4361C;DyÈ;39,N14C;5.­ * I@cÝ6}6Ö6Ö6քt} @À»’PQ v '?C‰< '?C„< 14CËä‘F27/m*4361C;gD [7JSHhÖo[7]O[7JDEb7¯GÈ;39W, s 14C;5. *  ã Ý }6Ö6Ö6ք} ãjÁ ü>~ Ž/’Æ*>0)/;F2F2(+F2HÜ1>'?3Ü*>/;K3*40)/;,N3Æ1>'2/1')/1/;F C;5>1>'?CPF2C;5.KL/;:c*4361=C;DÏÈ;39,N14C;5.*y(+*/L*>361C;DZ:+(+F?39/5.:+B(+F27?360b39F27239Fq18È;39,N14C;5.*@39/;,.'Æ')/9Èv(+F?HLF?C;5.K C;D ® Q Å 365.(uDB1>'2/1=,NCPK0):+3N’ FrA2KXI‘365z*,6/;FIb3´5>36025>39*439Fo14397IrB KL/145.(+,N39*Èv(+/ å ¢ … à ÕâZˆ Æ Á …ˆ § … ˆ Å '™1>'?3 A2*>A2/;:O5.A2:+39*JC;D=,NCPKL0):u3N’™FrA2KXI‘365z*X/;F27 C;D=K/145.(¡’^KL/;F2(+0)A2:+/1>(uCPF)*6x›(éQê3;QË,z'?39¼, ‰/;7272(+1>(uCPFExZ/;F27 K!A2:u1>(u0):M(+,6/1>(uCPFEQ ¤ !0Ì"¥Çšœr— žo| î {´(uÈ;39F/L14C;Š0 sñ,NCPK0)/;F2(+CPFKL/145.(¡’ ²³³ § …)Ý § … Ä Ö6Ö6Ö § … Ý § … µ ¶¶ ³³ ® ¨ Ö6Ö6Ö ¨ ë ² ¨ ë ¶¶ |¢ QQ QQ QQ QQ QQ ´ ¨ ¨ Ö6Ö6Ö ® ¨ ¸ v '?C‰'2/1=(+D;`Ü(+*/;Fn39(uH;39FoÈ/;:+A?3C;DÇ|ç1>'?39F¯ ¢UÐÇ` ë ² Ý Ö6Ö6ÖÈ` ® ԍ>™(+*1>'?3,NC;5.5>39*40bCPF272(+F2H!39(+H;39FqÈ;39,N14C;59Q

©;©