22 Vetores Matrizes

Prévia do material em texto

�����������	
�������
�������
������������������
�
���������������������	�
��
����
���
����� !"#$!%	&'(&%)�%*&'&+,-$�%
./012343567/08349:809;<=>33=>3<?;=@9190AB0C343317/9@91356732D74EB>913/3
;72=567/0=>33>C23D3>3/0C47F20>3;<>3;?9A;=@9190AB0C34340;72804=>D43A/0
AG>047/0C47F20>3;17>C=B3197A39;HI>3D9A0<C740J0>C27<17>7@34E3>7;C34317A;B4=94
=>32D749B>7<K=020;;07;A7>0/0LMMC0;;73;09>C49>9;;0=>4023BN497/0;B0;>0;>7;
A7>0;<>3;74/0A3/7;32@3F0B913>0AB0HO67;0493=>3B340@3;9>C20;<C79;B04E3>7;K=0
/0@9A94LMM8349:809;/7B9C729B0432<17>7?>7;B43/73F39J7P
�Q$'(R&����
ST UVWXYZ[\X_`abcade^
fT gUY
hT i`jdSkijdfkijdhkijdlkijdmkTTTkijdlnnkijdmoopebqdrse
lT b`btbi
mT VuZUv`ijdSk`ijdfkTTTk`ijdmoow
xy TTT
{H |Z\UVWXYZ[\X
}7A;9/0407B3>3A~7/732D749B>7<07B43F32~7F43532A010;;:497C34317A;B4=E27H€343
40;72804C47F20>3;17>70;B0<07=B47;<0J9;B0>3;‚ƒ„…†„‡„‰Š†‹‚Š‚‡H./012343567/0
=>38349:8029A/0J3/317440;C7A/0<A3804/3/0<Œ/012343567/08:493;8349:809;1=7
9/0AB9@913/74/9@0403C0A3;C74=>Ž‘’“H”EA/91017440;C7A/03=>83274A=>?4917
17>053A/7C74•H}3/38349:8029A/0J3/3C7/04010F04832740;A7/0174404/732D749B>7
17>7;0@7;;0=>38349:80217>=>H
������ !"#$!%
-–$Q�–�%�-!–!'$-%!&-�!%—�$)& $%˜
™349:809;9A/0J3/3;17>=>3GA913/9>0A;67<B3>F?>17A~019/3;17>7†š›ƒ†‡<;67
40@040A193/3;C74=>GA917EA/910H.;9AB3J0C343/012343567?P
œbd`qbžbtsirŸ¡gu[XY¢œ[U\U£¤XŸ¥¦uœqb§iŸ
U¨\U£¤X¢©ª««©|¥¬­©Z¬©UVXYZ£Z®ZUV¦X£¦Z®uu©|gUVXY|Z£UV¦X£¦Z®u«
�Q$'(R&���°
±y ²³´ ³µ¶·µ¸ ¹º»¼yym¥½¾ª¿¨¾ªÀÁ
Ây ùĵŶ·µ¸ ¹º»¼yyL¥½¾ÆÇÀÇƨ¾À¾
./012343567319>317440;C7A/0Œ/012343567/0•M8349:809;PA7>0;ȕÉ<A7>0;ÈÊÉ<
A7>0;ÈËÉ<A7>0;ÈÌÉ<A7>0;ÈLÉ<9/3/0;ȕÉ<9/3/0;ÈÊÉ<9/3/0;ÈËÉ<9/3/0;ÈÌÉ09/3/0;ÈLÉH
€343;03B49F=94=>832743=>020>0AB7/780B74/080>7;=B929Í347;0D=9AB0C3/467P
œbd`qbžbtsirŸ¢œÎXÏZÐÑXŸ¥ÒӜaseirŸ
�Q$'(R&���Ô
ST i`jdÕÖSלØÙÚiÛisÜbeasÝ
fT bsdÕÖSלØhm
hT i`jdÕÖhלØÙÞsrbsߧsrdtbsÝ
lT bsdÕÖhלØbsdÕÖS×
mT bϯm
àT bsdÕÖbלØlm
�����������	
�������
�������
������������������
���������������������� � 
�!"#$%&'(�)
*+,-./01-345+641750-.89:;<=>5?@-A/BC5A5-5AD.575E*A5,4/.F5+5D-G0H
34HG0-A7H+-.5A>589:;<=AI-G5,H0/7-A55AD.57H5A0H/GJ-.1HBI-E
KL MNOPQRSTPVWXSPQXYV
ZL [M\
]L _^` abcd[efg\hKLLijke\eMl
mL nFD-G0HoG5,pqrfeq\g
sL RtRuRP
?E D-G0HoG5,vwx
yL z{Q{R|XK{SXi}{u{
~E +5/H^ _` abc€/‚
ƒL YX_` abc€/vxXtS{P
„xE D-G0HoG5,vwD-G0HoG5,…„
KKL }RTYX
KZL }RTz{Q{
K]L z{Q{R|XK{SXi}{u{
„†E 5AD.57H+^ _` abc€/‚
KsL }RTz{Q{
KiL XYuQXW{‡Vˆ-0H+>5G‰15.-AG5,H0/7-ApŠFD-G0HoG5,‹
KyL }RT{NOPQRSTP
'(�ŒŽ‘’"“
”•"!Ž•Ž“–•#"”“&”Ž“—�Ž˜™"“š
›H./œ75/A/G>5H>HAD-1>4HA>/15GAC5AF0H1žŸ1D-G 5D/>HD-1-¡¢£¤¥¦§¨ FAI-
.5J5.5GD/H>HA@-.>-/A©G>/D5AFDH>H34H+D-15BHG>-@-.„E*A/G0H5@H.H>5D+H.HBI-Ÿp
ª«¬­®¯«°«±²¬³´µ·¹º»¼½ªº¾¿¾ÀÁ»ÂµÃªº¾¿¾ÀÁ»ÄµÅƹª«È³µ
ɾ¿¾ÀÁ»½ÊËÌÌÊÍÅÎÏÊÐÎʾѻ¼ÐÀÐÒоÑÆ»ÓÀÆÐÒ¹¹Ê;ѻ¼ÍÐÀ¾ÑÆ»ÓÀÆÐÒ¹Ì
�!"#$%&'(�Ô
ÕeÖÖgMÖd[efg\×ØÙÙÚÃØÙÙÛÜÝÞßàáàßÉÞáÞ
*>5D+H.HBI-HD/1HD-..5A@-G>5â>5D+H.HBI->5?7H./œ75/Apã;ää=åä×ØÃØÜFã;ää=åä
×ØÃÚÜFã;ää=åä×ØÃÛÜFã;ää=åä×ÚÃØÜFã;ää=åä×ÚÃÚÜF5ã;ää=åä×ÚÃÛÜÙ
æH.HA5H0./ž4/.417H+-.H415+515G0->-750-.>5751-A40/+/çH.-A5,4/G05@H>.I-p
ª«¬­®¯«°«±²¬³´µ½ªè»éÐêë»ÂµÃìè»éÐêë»ÄÏÅìíªî²ï³´µ
�!"#$%&'(�(
ÕeÖÖgMÖ×ØÃÛܪðñò³®­¯ó
�����������	
�������
�������
������������������
���������������������� � 
�!"#$%&'(�)
*+,-./01-345+6417170./896:7+-.5;<=>=?5@7+@4+77;;-17;A
7CD7+/EF7GD5:7+-.5;H
ICD7@-+4E7JD5:7+-.5;H
@CD7D/7,-E7+K./E@/K7+H
DCD7D/7,-E7+;5@4EDL./7H5
5CD50-D-;-;5+515E0-;D7170./8M
NO PQRSTUVWSYZ[VTU\Y
]O P^_
O` abcdefgijkl_mNOO`nNOO`opj_jPq
rO stuvcwxyv=>stuvzt{|xv}>stuv~wv€wx‚>stuv~wvsƒ‚|>stuv„|…t†_jPq
‡O w>ˆ†‰Škj‰_l‹‹SŒŽU‘Œ‘W’T‘UŽV‘UTS
“O UŽUUS
”• stuvcwxyv=–—˜
™• stuvzt{|xv}–—˜
š• stuv~wv€wx‚–—˜
›˜• stuv~wvsƒ‚|–—˜
››• stuv„|…t–—˜
N]O œ[T[U‘N[V‘[[
N`O œ[T[ž‘N[V‘[[
NrO jŒT‘Ÿ[ Y~ww¡ƒ|u¢v{t£vvvuv¡w¤Y¥
N‡O q‘U[ abcdefg¦w>ˆ§¥
›¨• stuv„|…t–—abcdefg¦w>ˆ§©stuv„|…t
NªO Œ‘U«`‘ŽV[S
›™• stuvcwxyv=–—abcdefg¦w>ˆ§©stuvcwxyv=
N¬O UWŒ‘
]­O Œ‘ž«]‘ŽV[S
}›• stuvzt{|xv}–—abcdefg¦w>ˆ§©stuvzt{|xv}
]]O UWŒ‘
]`O Œ‘U«ž‘ŽV[S
}®• stuv~wv€wx‚–—abcdefg¦w>ˆ§©stuv~wv€wx‚
]‡O UWŒ‘
]“O Œ‘ž«r¯U‘ŽV[S
}”• stuv~wvsƒ‚|–—abcdefg¦w>ˆ§©stuv~wvsƒ‚|
]°O UWŒ‘
]¬O UW’[T[
­`O UW’[T[
N`O œ[T[U‘N[V‘[[
]`O ’[T[ž‘N[V‘[[
==• ƒs‚ƒ¢v{<abcdefg¦w>ˆ§?
r`O UW’[T[
‡`O UW’[T[
“`O ‘ŒT‘Ÿ[Q Ygtuv…ƒ¡t…tstsƒ{ƒuƒx¡ts±²>stuv„|…t¥
ª`O ‘ŒT‘Ÿ[Q Ygtuv…tsƒ{ƒuƒx¡ts…v{wxyv=±²>stuvcwxyv=¥
°`O ‘ŒT‘Ÿ[Q Ygtuv…tsƒ{ƒuƒx¡ts…v‚t{|xv}±²>stuvzt{|xv}¥
¬`O ‘ŒT‘Ÿ[Q Ygtuv…tsƒ{ƒuƒx¡ts…v…wvtxv{£wx‚w£v{±Yn
ŒSW[pU[RœTUŽ¥
r­O ‘ŒT‘Ÿ[Q Ygtuv…tsƒ{ƒuƒx¡ts…v…wvtxv{sƒ‚|x…³wv±Yn
ŒSW[pU[RŒ‘´¥
µ¶M UW[QRSTUVWS
·¸ ¹º»¸¼½¾¸ »¿À¿Áº¼ÂÃÄÅÆÁÂÃÇÈ
Éù»Áʽ¾¸ »¿À¿Áº¼ÂÃÄÅÆÁÂÃÇË
�����������	
�������
�������
������������������
���������������������� ��
	 !"#$%&'()*#&+�,*+-.-"&/
1234565789
:<=>?@ABCDBEFG?HIDGJC@EKCDA@IG?LMNOP@@=>?@ABBQG=HRSGT@>BTB@E@D@UIGHFCBEBNOT@=I@
A@IG?V
123456578W
:<=>?@A@?CDBEFG?HIDGJC@EKCDA@IG?YMNOOP@G@=>?@A@VZC[=IHICB\B=@FCH?\IGTG=G=ABEG?@=
UCEG=T@YQG?N@@=>?@ABUGABD@UI@GA@IG?YV
123456578]
:BRBCDBEFG?HIDGJC@E@HBNOOABEG?@=@G=@=>?@ABUBG?T@D>GUI?_?HBJC@aG?BDTHFHIBTG=V
123456578c
d<=>?@A@?CDBEFG?HIDGJC@EKCDA@IG?eMfOP@G@=>?@A@V<U>GUI?@\B=@FCH?\GD@UG?@E@D@UIG@B
=CBQG=HRSGUGA@IG?e@@=>?@ABghiD@UG?@E@D@UIGT@ejkVVV@B=CBQG=HRSGjVVVhV
123456578l
d<=>?@A@?CDBEFG?HIDGJC@EKCDA@IG?eMmOP@G@=>?@A@Vn?GJC@\B=@FCH?\GNo@E@D@UIG>GDG
pEIHDG\Gmo>GDGQ@UpEIHDG\@I>BIjGNOo>GDGNNo@@=>?@ABGA@IG?eB==HDDGTHaH>BTGV
123456578q
d<=>?@ABCDBEFG?HIDGJC@F@?BG=NOQ?HD@H?G=UpD@?G=Q?HDG=B>HDBT@NOO@G=B?DBr@UB@DCD
A@IG?stuvw@=>?@A@UTG\UGaHUBE\GA@IG?sV
123456578x
y<=>?@A@?CDBEFG?HIDGJC@EKCDA@IG?zMN{PJC@jGFB[B?HIGT@CDI@=I@T@EGI@?HB@=QG?IHAB\
>GUI@UTGG=ABEG?@=NM>GECUBNP\mM>GECUBmP@{M>GECUBTGD@HGPV|@?\B=@FCH?\QB?B>BTBBQG=IBTG?\G
UpD@?GT@=@C>B?ISG@CDA@IG?}@=QG=IB}MN{PV~@?HaH>B?QB?B>BTBBQG=IBTG?GUpD@?GT@B>@?IG=@
@=>?@A@?GUpD@?GTGBQG=IBTG?@=@CUpD@?GT@B>@?IG=VZ@IHA@?N{B>@?IG=\B>?@=>@UIB?BD@U=BF@Dg
hzLeL€i}\L}L‚<eZhV
123456578ƒ
y<=>?@A@?CDBEFG?HIDGJC@EKCDA@IG?LMN„P@G@=>?@A@Vi?T@U@B=@FCH?G=@E@D@UIG=T@L@D
G?T@D>?@=>@UI@@@=>?@ABUGABD@UI@LV
…†‡ˆ‰Š‹Œ
<=>?@A@?CDBEFG?HIDGJC@EK\QB?BCDA@IG?~M{OP\AHUI@ABEG?@=JC@G>CQB?SGB=mOQ?HD@H?B=QG=HR@=
TGA@IG?~Vi?T@U@\B=@FCH?\G=@E@D@UIG=T@~@DG?T@D>?@=>@UI@V|@HB\B=@FCH?NOABEG?@=L\CD
QG?A@r\@HU=H?BŽG=UB=QG=HR@=BT@JCBTB=TGA@IG?~\T@aG?DBJC@GD@=DG>GUIHUC@G?T@UBTG@D
G?T@D>?@=>@UI@V<=>?@ABGA@IG?~B==HDaG?DBTGV
�����������	
�������
�������
������������������
���������������������� � 
	"#$%&'()*�"%+$,�-.+/0/$(1
34567879:;
<>?@ABCBADEFGHIAJKEILFAFFAEFMBNFACFGIAB?JNKBJAI?BEDEFEFKAJMOPQRSTU?BHDJAQ@FG@DGFAF
EVWJFWI?CFGIAB?LFAB?@INKJWI?NFEFKAJMBB?@ABCBA?BD@INKBXWIT
34567879:Y
<>?@ABCBADEFGHIAJKEILFAFGBADEFEFKAJMOZQ[S@INKBNWICFGIAB?JNKBJAI?O?DLIA\DBI?CFGIAB??]I
WJ?KJNKI?STUL^?QBN@INKAFAIEBNIACFGIA@INKJWINFEFKAJMB?DFLI?J_]IT
34567879:
<>?@ABCFDEFGHIAJKEI\DBGaDEFEFKAJMbOPQPSB@FG@DGFF??IEF?c
FSWFGJNdF[WBbT
eSWF@IGDNFfWBbT
@SWFWJFHINFGLAJN@JLFGT
WSWFWJFHINFG?B@DNWgAJFT
BSWBKIWI?I?BGBEBNKI?WFEFKAJMT
hS>?@ABCFB?KF??IEF?BFEFKAJMT
34567879:i
j�klmnonmpqrstumvwquxpnsypqrqrwmvz{| } ~nlmvronwumnk€�| ~}€| ~xpnlu‚wn‚ƒrq
mnk„nlwvorqn‚wnrkkuqrk…rksv‚ƒrkn…rklusp‚rk…n{†�klmnonmrqrwmvznukonwumnklmvr…uk†
34567879:‡
j>?@ABCBADEFGHIAJKEI\DBGaWDF?EFKAJMB?ˆ‰Š‹ŒŽBˆŠ‹ŒŽB@AJFc
FSEFEFKAJM‘‰\DB?B’FF?IEFWBˆ‰Bˆ
eSEFEFKAJM‘\DB?B’FFWJhBABN_FWBˆ‰@IEˆ
>?@ABCBAF?EFKAJMB?GJWF?B@FG@DGFWF?T
34567879:“
j>?@ABCBADEFGHIAJKEI\DBGaDEFEFKAJMbORQRSB@FG@DGFF??IEF?WF?LFAKB?dF@dDAFWF?T>?@ABCBA
FEFKAJMbBF??IEF?@FG@DGFWF?T
34567879:”•–FKBIAJFWB—J?KBEF?WBhJNB˜?BBGBEBNKIE™NJEFšWBDEFEFKAJMQIEBNIABGBEBNKIWFGJNdFBE\DB
?BBN@INKAFIEFJIABGBEBNKIWFEFKAJMT>?@ABCBADEFGHIAJKEI\DBGaDEFEFKAJMUO›œQ›œSBWBKBAEJNF
IBGBEBNKIE™NJEFšWB?KFEFKAJMQB?@ABCBNWIFEFKAJMUBFLI?J_]IWIBGBEBNKIE™NJEFšT
34567879:
•>?@ABCFDEFGHIAJKEI\DBIAWBNBI?BGBEBNKI?WB@FWFGJNdFWBDEFEFKAJMbž›œQ›œŸT
�����������	
�������
�������
������������������
���������������������� � 
!
!!
!"#$%&'(
*$+,#-#,./%01(,'2/(3.#1#,###$+,#-%(3.%4,%4(/51'+(4#(,4#/67
8/3.%4,%4(/51'+(4#(,4#/9:$#94(9./9;/#,(</=%,>?./%,,%9@(4#9;/#,($4#A%2?9
B
#/
./%/%2,'C3.%4,%4%4#2%0/(4(3.#%$(/%4#+%4%0'9D%E+(0.9%(.4'%1(9%0?%/#$/%7
F G 6
H G I
B J I
A K B J
F L A
M&'1.,%/($2,%./3.%4,%4(/51'+(4#(,4#/F7M,#1,%4#&(,/%NO(?,#0%2'-%/#92#&5+'04#$#,
-#,'&'+%4%PQ(/#+#+(/(A9(/#'(4%=,'/#',%0'9D%7R=%,2',4%<$'1%=%,%+'/%#=%,%S#$3.#,4%
4'%1(9%0/#92#:3.%94($%',4(3.%4,%4($.=(9D%3.#($0%4($$.=#,'(,#'9&#,'(,#$2O(.9'4($#($0%4($
#$3.#,4(#4',#'2(4%/#$/%&(,/%>7*/+%4%3.%4,%4(3.#=%$$%,+(0(3.#(-%0(,4(3.%4,%4(%92#,'(,
%+,#$+'4(4#./%.9'4%4#7T.%94(%2'91',./3.%4,%4(@5=,##9+D'4(E4#$N%./3.%4,%4(#(=,##9+D%
#+(92'9.#$#1.'94(%4'%1(9%0%2?2#,+(0(+%4((-%0(,9
B
7
	UVWXYZ[\]Y_UZ`[aWXb[�cdaefeW[g
ijklmnmopq
r*$+,#-#,./%01(,'2/(=%,%4#2#,/'9%,$#./4#2#,/'9%4(9;/#,('92#',(?=%,(.</=%,782'0'C%,
./$.s%01(,'2/(4#&.9NO(3.#,#2(,9%./-%0(,0t1'+(=%,%'94'+%,$#(-%0(,,#+#s'4(?=%,(.9O(7
ijklmnmopv
r*$+,#-%./%01(,'2/(3.#0w./9;/#,(9O(4#2#,/'9%4(4#-%0(,#$/E2(4($'92#',($#=($'2'-($E./
-%0(,4#+%4%-#CE#E$#/xAJ.2'0'C%./$.s%01(,'2/(4(2'=(&.9NO(3.#+%0+.0%(&%2(,'%04#/E#+%$(
+(92,5,'(E.2'0'C%./$.s%01(,'2/(4(2'=(&.9NO(=%,%(s2#,(9;/#,(4#4'-'$(,#$4#/:3.%92($
4'-'$(,#$/=($$.'>7*$+,#-#,+%4%/0'4(#$#.&%2(,'%0(.$#.9;/#,(4#4'-'$(,#$+(/./%/#9$%1#/
%4#3.%4%y7z#$2#+%$(E2#/($./=,(1,%/%=,'9+'=%0#4('$$.s%01(,'2/($7
ijklmnmop{
|*$+,#-%./%01(,'2/(3.#%=,#$#92#.//#9.+(/2,w$(=N}#$P
A~9$#,',
B~€#/(-#,
I~*$+,#-#,9%#0%(‚#2(,
G~ƒ%',
T.%94(&(,#$+(0D'4%%(=NO(9;/#,(AE./%$.s,(2'9%+D%/%4%„…†‡ˆ‡4#-#'9$#,',./#0#/#92(
:9;/#,(>#/./-#2(,7M$.s,(2'9%4#-#,#+#s#,=(,=%,‰/#2,((9;/#,(%$#,'9$#,'4(E%=($'NO(
:<94'+#>%$#,'9$#,'4(E(2%/%9D(4(-#2(,#(9(/#4(-#2(,7