Informe Proyecto Progra Calculadora Matrices (3)

UNIVERSIDAD CENTRAL DEL ECUADOR FACULTAD DE INGENIERÍA EN CIENCIAS FÍSICAS Y MATEMÁTICAS

ÍNDICE

PROGRAMACIÓN 1 INGENIERO: WAGNER WAGNER VLADIMIR LUCERO NAVARRETE NAVARRETE ELABORACIÓN DE UNA CALCULADORA DE OPERACIONES BÁSICAS ENTRE MATRICES EN TRES LENGUAJES DIFERENTES (VISUAL BASIC, C++, JAVA)

AUTORES: BENALCAZAR FRANK BUNCE SANTIAGO CAIZA PEDRO CALDERÓN KEVIN NARANJO JEFFERSON SARANGO KELL DE JULIO DE !"1#

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INTRODUCCION ..................... ................................ ..................... ..................... ..................... ..................... ........................................ ............................. 3 IMPORTANCIA .................... ............................... ..................... ..................... ..................... ..................... ..................... ..................... .......................3 ............3 OBJETIVOS .................... ............................... ...................... ..................... ..................... ..................... ..................... ..................................... .......................... 4 Objetivo gee!"#$.................... ............................... ..................... ..................... ..................... ..................... ..................... ............................. ................... 4 Objetivo% e%&e'()i'o%$..................... ................................ ..................... ..................... ..................... ..................... ................................. ...................... 4 DESARROLLO DEL CONTENIDO.................... ............................... ..................... ..................... ....................................... ............................ 5 MATRICES EN PROGRAMACI*N$ ..................... ............................... ..................... ................................................ ..................................... 5 OPERACIONES BÁSICAS DE MATRICES$ .................... ............................... ..................... ...................................... ............................ 6 S+," - Re%t" .e ,"t!i'e%$.................... ............................... ...................... ..................... ................................................ ...................................... 6 Eje,&#o$.................... .............................. ..................... ..................... ..................... ...................... ..................... ....................................... ............................. 6 M+#ti&#i'"'i/ .e ,"t!i'e%$..................... ................................ ...................... ..................... .............................................. .................................... 6 P!o&ie.".e% .e #" ,+#ti&#i'"'i/ .e ,"t!i'e%$..................... ............................... ..................... ..................... .........................7 ...............7 TIPOS DE DATOS$ DATOS$..................... ............................... ..................... ..................... ..................... .............................................. ................................... 7 VISUAL BASIC$..................... ............................... ..................... ..................... ..................... ..................... ..................... ..................... ..................... ........... 9 De'#"!"'i/ .e #"% v"!i"b#e%$.................... ............................... ..................... ..................................................... ........................................... 9 Di,e%i/ .e #" ,"t!i0 A - .e #" ,"t!i0 B e ig!e%o$..................... ............................... ...............................10 .....................10 Me1 .e o&'ioe%$..................... ............................... ..................... ...................... ..................... ..................... ..................... ..................... ........... 11 C"%e 2.................... ............................... ..................... ..................... ...................... ..................... ..................... ..................................... .......................... 12 C"%e 3.................... ............................... ..................... ..................... ...................... ..................... ..................... ..................................... .......................... 13 C"%e 4.................... ............................... ..................... ..................... ...................... ..................... ..................... ..................................... .......................... 13 C"%e 5.................... ............................... ..................... ..................... ...................... ..................... ..................... ..................................... .......................... 14 I,&!e%i/ .e #"% ,"t!i'e%$ A - B6..................... ................................ ..................... ..................... ..................... ........................ .............. 14 I,&!e%i/ .e #" M"t!i0 Re%+#t"te6.................... ............................... ..................... ..................... .................................. ....................... 15 A''i/ .e #" b".e!"$.................... ............................... ...................... ..................... ..................... ....................................... ............................ 15 C..................... ............................... ..................... ..................... ..................... ..................... ..................... ...................... ..................... ............................ .................. 18 De'#"!"'i/ .e #"% v"!i"b#e%$.................... ............................... ..................... ................................................... ......................................... 19 Ig!e%o - #e't+!" e C..................... ................................ ...................... ..................... ..................... ..................... ........................... ................. 19 Ig!e%o - #e't+!" .e ."to%..................... ............................... ..................... ..................... ............................................ .................................. 20 Ci'#o% .e !e&eti'i/ o b+'#e%..................... ............................... ..................... ..................... ...................................... ............................ .. 21 Ig!e%o .e #"% ,"t!i'e% A - B...................... ................................ ..................... ..................... ..................... ............................. .................. 21















E# '"%e 3 .e# ,e1.................... .............................. ..................... ...................... ..................... ..................... ................................. ...................... 25 E# '"%e 4 .e# ,e1.................... .............................. ..................... ...................... ..................... ..................... ................................. ...................... 26 E# '"%e 5 .e# ,e1.................... .............................. ..................... ...................... ..................... ..................... ................................. ...................... 27 I,&!e%i/ .e #" )#"g..................... ............................... ..................... ..................... ................................................... ......................................... 28 I,&!e%ioe% .e #"% ,"t!i'e% A - B..................... ................................ ..................... ..................... ..................................29 .......................29 I,&!e%i/ .e #" ,"t!i0 !e%+#t"te..................... ................................ ..................... ............................................. ................................... 30 JAVA JAVA 8NETBEANS9 8NETB EANS9$$..................... ................................ ..................... ..................... ..................... ..................... ..................... ........................ .............. 31 :i%to!i" .e J"v"$..................... ................................ ..................... ..................... ..................... ..................... ..................... ...........................31 .................31 E%t!+'t+!" .e + &!og!"," e J"v"$..................... ............................... ..................... .............................................. ................................... 32 C"#'+#".o!" .e O&e!"'ioe% B;%i'"% .e M"t!i'e% J"v"$.....................................................33 De'#"!"'i/ .e v"!i"b#e%..................... ............................... ..................... ..................... ..................... ..................... ............................33 ..................33 Me%"je .e Bievei."$.................... ............................... ..................... ..................... .................................................. ....................................... 33 Di,e%i/ e ig!e%o .e #"% M"t!i'e% A - B$...................................................................34 Me1 .e o&'ioe%$.................... ............................... ..................... ..................... ..................... ..................... ..................... ......................... ............... 36 C"%e 2$..................... ................................ ..................... ..................... ..................... ..................... ................................................. ...................................... 36 C"%e 3$..................... ................................ ..................... ..................... ..................... ..................... ................................................. ...................................... 37 C"%e 4$..................... ................................ ..................... ..................... ..................... ..................... ................................................. ...................................... 38 C"%e 5 - .e)"+#t$...................... ................................ ..................... ..................... ..................... ..................... ..................... ..................... ................ ...... 39 I,&!e%i/ .e #"% ,"t!i'e% A - B$..................... ............................... ..................... ..................... ......................................40 ............................40 B".e!"$..................... ................................ ..................... ..................... ..................... ..................... ............................................... .................................... 41 I,&!e%i/ .e #" ,"t!i0 !e%+#t"te$..................... ................................ ..................... ..................... ..................... ..................... ................. ...... 43 CONCLUSIONES$ .................... ............................... ...................... ..................... ..................... ..................... ..................................... ........................... 44 RECOMENDACIONES$ .................... ............................... ..................... ..................... ..................... ..................... ............................... .................... 45 BIBLIOGRAFIA..................... ............................... ..................... ...................... ..................... ..................... ..................... ............................. ................... 46 Lib!o e Ig#<%$..................... ................................ ..................... ..................... ..................... ..................... ..................... ............................ .................. 47















INTRODUCCION E# &!o-e'to &!o-e'to e%t; .e%ti". .e%ti".oo " e=&#i'"! e=&#i'"! " +%+"!io% +%+"!io% 'o 'oo'i 'oo'i,ie ,ieto% to% ite!,e.io ite!,e.io%% o +#o% e# .e%"!!o##o .e + &!og!"," >+e e,&#e" ,"t!i'e% - "&#i'" o&e!"'ioe% b;%i'"% o )+.",et"#e% 8'"#'+#".o!"96 8'"#'+#".o!"96 Se e,&#e" &"!" e##o #o% e.ito!e% .e '/.igo >+e %e ?" +%".o " #o #"!go #"!go .e# "'t+"# "'t+"# %e,e% %e,e%t!e t!e 8C@@ 8C@@ vi%+"# vi%+"# b"%i', b"%i',"'! "'!o% o% j"v" j"v"etb etbe" e"%9 %966 E e# 'o 'ote tei.o i.o %+b%e'+ete %+b%e'+ete %e e'+et!" .e ,"e!" .et"##"." - 'o #o% eje,&#o% 'o!!e%&o.iete% #" '!e"'i/ .e# &!og!"," e '+e%ti/6 A.e,;% %e i'#+-e !e)e!e'i"% b;%i'"% %ob!e #o >+e "b"!'" #o% "!!eg#o% .e ,"t!i'e% >+e e% #o >+e .et"##" +e%t!o &!o-e'to6 L" bib#iog!")(" "+to!e% - )+ete% .e 'o%+#t" %e e'+et!" "e=".o% e e# ,i%,o6

IMPORTANCIA Po.e,o% ".e,;% .ete!,i"! >+e #" #/gi'" .e &!og!","'i/ %e "&#i'" .e ig+"# )o!," &"!" !e%o#ve! + ,i%,o &!ob#e," e .i)e!ete% #eg+"je% - >+e e# 1i'o &+to " to,"! e '+et" e% #" t!"%i'i/ e #" %it"=i% e,&#e"."6 Debe,o% to,"! e '+et" ".e,;% #"% vet"j"% - .e%vet"j"% >+e o)!e'e '"." #eg+"je .e &!og!","'i/ 'o,o !e.+''i/ .e 'o%+,o .e ,e,o!i" ve#o'i.". .e eje'+'i/ - 'o,&#eji.". .e #" !e."''i/ ! e."''i/ .e# '/.igo6 A.e,;% &o.e,o% &e!'"t"!o% .e #o% +%o% >+e &+e.e ."!%e " +" ,"t!i0 - #" i)ii.". .e "!!eg#o% >+e &o.e,o% "&#i'"! " #" !e%o#+'i/ .e .i)e!ete% &!ob#e,"%6















TEMA ELAB ELABOR ORAC ACI* I*N N DE UN UNA A CALC CALCUL ULAD ADOR ORA A BÁSI BÁSICA CA DE MAT MATRICE RICES S EN TRES TRES LENGUAJES DIFERENTES DIFEREN TES 8C@@ VISUAL BASIC JAV JAVA9

OBJETIVOS O$%&'* &&-./: E#"bo!"! +" '"#'+#".o!" .e o&e!"'ioe% b;%i'"% et!e .o% ,"t!i'e% e,&#e".o .i%tito% ti&o% .e #eg+" #eg+"je% je% .e &!og!" &!og!","' ,"'i/ i/ &"!" &"!" &o &oe! e! e &!;'ti &!;'ti'" '" #o% 'oo' 'oo'i,i i,iet eto% o% &!evio &!evio%% %ob!e %ob!e "!!eg#o% .e ,"t!i'e%6

O$%&'*0 &0&2342*0:



E=&#i'"! "# +%+"!io #"% '"!"'te!(%ti'"% .e '"." +o .e #o% &!og!","% >+e ite!viee e #o% t!e% ti&o% .e #eg+"je% e,&#e".o% e e# &!o-e'to6



D"! " 'oo'e! e# )+'io",ieto .e +e%t!" '"#'+#".o!" " b"%e .e + t+to!i"# &"!" #o% +%+"!io% 'o 'oo'i,ieto ,e.io o +#o %ob!e e# te,"6















DESARROLLO DEL CONTENIDO MATRICES EN PROGRAMACIÓN: U" ,"t!i0 e% +" e%t!+'t+!" .e ."to% o ,;% t<'i'",ete + e%&"'io .e ,e,o!i" >+e &e!,ite "#,"'e"! +" 'o#e''i/ .e e#e,eto% to.o% .e# ,i%,o ti&o6 A .i)e!e'i" 'o #o% "!!eg#o% e%t; e >+e e #"% ,"t!i'e% #o% e#e,eto% o e%t; o!g"i0".o% #ie"#,ete #ie"#,ete %io >+e %+ o!g"i0"'i/ e% bi.i,e%io"# e% .e'i! e )i#"% - 'o#+,"%6 Coviee i,"gi"! +" ,"t!i0 'o,o +" o!g"i0"'i/ .e 'e#."% .e ,e,o!i" o '"%i##"% e '"." +" .e #"% '+"#e% %e &+e.e g+"!."! + e#e,eto .e #" 'o#e''i/6 A.e,;% e% +%+"# .ib+j"!#" 'o,o #o i#+%t!" #" )ig+!" %ig+iete$ 

2

3

4

5



 2 3 4 E%t" )ig+!" !e&!e%et" +" ,"t!i0 .e '+"t!o )i#"% 8+,e!"."% ve!ti'"#,ete .e  " 49 %ei% 'o#+,"% 8+,e!"."% ?o!i0ot"#,ete .e  " 96 E '"." +" .e #"% 35 'e#."% o '"%i##"% %e &+e.e g+"!."! + ."to6 L" 56&07 o t","o .e +" ,"t!i0 e% e# 1,e!o )i#"% &o! e# 1,e!o .e 'o#+,"%6 Debe %e! '#"!o eto'e% >+e #" )ig+!" "te!io! e% #" g!;)i'" .e +" ,"t!i0 .e .i,e%i/ 5=6 L" +,e!"'i/ .e #"% )i#"% - #"% 'o#+,"% .ete!,i" >+e '"." +" .e #"% '"%i##"% .e +" ,"t!i0 tiee "%o'i".o% .o% 1,e!o% >+e #" i.eti)i'" .e ,"e!" 1i'"6 A e%to% 1,e!o% %e #e% ##"," ##"," 352& 5& 4/. e 352& 5& 2*/86.  !e%&e'tiv",ete6 E e# %e+.o#eg+"je t",bi< e Vi%+"# B"%i' C @@ - J"v" #"% )i#"% - #"% 'o#+,"% %e +,e!" .e%.e 6 A?o!" ve!e,o% e# eje!'i'io >+e ?e,o% !e"#i0".o e# '+"# e% +" C"#'+#".o!" .e O&e!"'ioe% B;%i'"% et!e ,"t!i'e% e .i)e!ete% i.io,"% .e &!og!","'i/ 'o,o #o% %o$ Vi%+"# Vi%+"# B"%i' C @ @ - J"v" 8Netbe"%96

















Do% ,"t!i'e% .e #"% ,i%,"% .i,e%ioe% %e &+e.e %+,"! o !e%t"! #" %+," o !e%t" .e .o% ,"t!i'e% .e .i)e!ete .i,e%i/ o6 L" %+," - !e%t" .e .o% ,"t!i'e% .e #"% ,i%,"% .i,e%ioe% e% +" ,"t!i0 .e #"% ,i%,"% .i,e%ioe% - %e obtiee %+,".o o !e%t".o %+% e#e,eto% 'o!!e%&o.iete%$

E%&6/*: Re"#i'e #" %+," .e #"% ,"t!i'e%$

Ob%e!v",o% >+e #" %+," %( %e &+e.e !e"#i0"! &o!>+e #"% .i,e%ioe% .e #"% ,"t!i'e% 'oi'i.e "%($

M8/'/2.27 5& 6.'-2&0: Do% ,"t!i'e% A - B %o ,+#ti&#i'"b#e% %i e# 6&-* 5& 2*/86.0 5& A 'oi'i.e 'o e# 6&-* 5& 4/.0 5& B 6

M6 ;  ; M ;  < M 6 ;  E# e#e,eto 2% .e #" ,"t!i0 &!o.+'to %e obtiee 68/'/2.5* '"." e#e,eto .e #" 4/.  .e #" ,"t!i0 A &o! '"." e#e,eto .e #" 2*/86. % .e #" ,"t!i0 B - 086=5*/*06

















P-*&5.5&0 P-*&5.5 &0 5& /. 68/'/2.27 5& 6.'-2&0: A%o'i"tiv"$

A > (B > C) < (A > B) > C E#e,eto e+t!o$

A>I+e #" ,"t!i0 A6 No e% Co,+t"tiv"$ Co,+t"tiv"$

A>B@B>A

































VISUAL BASIC: E% + #eg+"je #eg+"je .e &!og!" &!og!","' ,"'i/ i/ >+e %e ?" .i%e .i%e".o ".o &"!" )"'i#it" )"'i#it"!! e# .e%"!!o##o .e "&#i'"'ioe% e + eto!o g!")i'o 8GUIGRAP:ICAL USER INTERFACE9 INTERFACE9 Co,o Hi.o% Hi.o% K Hi.o% NT o NT o %+&e!io!6

E e# &!e%ete "&"!t".o &!o'e.e!e,o% " #" e=&#i'"'i/ .e# &%e+.o'/.igo &"!" !e"#i0"! +" '"#'+#".o!" .e ,"t!i'e% e Vi%+"# B"%i'6 P"!" e##o .ivi.i!e,o% e# "#go!it,o e .i)e!ete% "&"!t".o%$

D&2/.-.27 5& /.0 .-.$/&0:

E e%te &+to %e .ebe .e'#"!"! to."% #"% v"!i"b#e% >+e ite!viee e# )+'io",ieto .e #" '"#'+#".o!" .e ,"t!i'e%6 P"!" e##o %e .ebe i'#+i! #" i%t!+''i/ Dim 8De'#"!" - "%ig" e%&"'io .e "#,"'e",ieto &"!" +" o v"!i"% v"!i"b#e%9 e +e%t!o eje,&#o .e'#"!",o% #"% v"!i"b#e% i, j, k, numfa, numfb, nunca, numcb, flag, opción - &"!" )i"#i0"! ."!e,o% e# ti&o .e v"!i"b#e e +e%t!o '"%o Integer 8-" 8-" >+e ".,ite ete!o%96 matrizA (300,300), (300,300), matrizB matrizB (300,300) (300,300) y T",bi< ,bi< .eb .ebe,o e,o%% .e'#" .e'#"!"! !"! #"% v"!i"b v"!i"b#e% #e% matrizA matrizC (300,300), matrizC (300,300),

t",bi< 'o #" i%t!+''i/ Dim - 'o %+ ti&o .e v"!i"b#e Double 'o #"

.i)e!e'i" >+e "# %e! + "!!eg#o .ebe,o% ."! %+ .i,e%i/ e% &o! e##o >+e %e "+,et" + &"!<te%i% e e# '+"# 'ote.!; e# 1,e!o .e )i#"% e #" &"!te i0>+ie!." - e# 1,e!o .e 'o#+,"% e #" &"!te .e!e'?"6

















D6&07 5& /. 6.'-? A 9 5& /. 6.'-? B & -&0*:

Uti#i0",o% #"% v"!i"b#e% numfa y numca &"!" #" 6.'-? A - numfb y numcb &"!" #"

6.'-? B 8>+e %i,bo#i0" e# 1,e!o .e )i#"% - .e 'o#+,"% .e #"% ,i%,"%9 - 'o #" "-+." .e #" )+' )+'i/ i/ InputBo! 8+e ,+e%t!" + ,e%"je e + '+".!o .e .i;#ogo e%&e!" " >+e e# +%+"!io e%'!ib" + te=to o ?"g" '#i' e + bot/96 It!o.+'i,o% #o% ,e%"je% 'o!!e%&o.iete% " #"% .o% v"!i"b#e% &"!" &e.i! "# +%+"!io >+e e%&e'i)i>+e + v"#o!$ "Ingre#e el n$mero %e fila# %e la matriz A", e "Ingre#e el n$mero %e columna# %e la matriz A" 6



















Do.e  %e +%" &"!" 'o'"te"! +" e=&!e%i/ " +" v"!i"b#e o &!o&ie.". - "%ig" e# !e%+#t".o " #" v"!i"b#e o &!o&ie.".6

M& 5& *2*&0: C75*: O&'i/  I&+tBo=8E#ij" #" o&'io$ @ C?!8249 @ 2$ %+," @ C?!8249 @ 3$ !e%t" @ C?!8249 @ 4$ ,+#ti&#i'"'io @ C?!8249 @ 5$ .ivi%/9 E# &!e%ete '/.igo i'#+-e #" i%t!+''i/ InputBo! "te% -" e=&#i'"." - e# %"#to .e #(e" >+e %e #og!" 'o *+ Cr('3) +-.



















Ca#e '

Con sus respectivas Instrucciones. Existirá el caso del sino Ca#e 1l#e

Co %+ i%t!+''i/ t",bi<6 Y e# /elect Ca#e )i"#i0"!; 'o #" I%t!+''i/ 1n% /elect.

E +e%t!o &!og!"," to.o% #o% '"%o% i'#+-e e# &!o'e.i,ieto &"!" &"!" '"." o&e!"'i/$ o&e!"'i/$

C.0& 1



















A# ig+"# >+e e #" %+," #" !e%t" %e ." e#e,eto e#e,eto 'o e#e,eto .e ",b"% ,"t!i'e%6

C.0& 

E e# '"%o .e #" ,+#ti&#i'"'i/ ii'i"#i0",o% e# e#e,eto .e #" matrizC(i , j)0 &"!" >+e '"." ve0 >+e %e !e'o!!" e# te!'e! Loo& ig!e%e %i ig1 v"#o! e% .e'i! e# 'e!o6 P"!" &o.e! "%ig"! e# v"#o! >+e #e 'o!!e%&o.e "# e#e,eto .e #" matrizC, %e %+," #o >+e tiee e# e#e,eto .e #" matriz C 8e 8e e%e ,o,eto -" >+e %e 'ovie!te e +" v"!i"b#e "'+,+#"tiv"9 " #" ,+#ti&#i'"'i/ .e #" )i#" .e #" matrizA &o! #" 'o#+," .e #" matrizB. 1 %

&o! e##o >+e !e'o!!e,o% t!e% Ci'#o% Re&etitivo% &"!" >+e e e# te!'e!o %e &+e." !e'o!!e! #" )i#" .e #" matrizA - #" 'o#+," .e #" matrizB



















Y e e# 1#ti,o '"%o tee,o% #" .ivi%i/ >+e t",bi< %e #" !e"#i0" e#e,eto &o! e#e,eto .e ",b"% ,"t!i'e%6 L" v"!i"b#e flag 8b".e!"9 8b".e!"9 'o##ev" %+ &!o'e%o >+e %e!; e=&#i'".o ,;% ".e#"te6

I6-&07 5& /.0 6.'-2&0: A 9 B

E e%t" i,&!e%i/ #o >+e e'e%it",o% e% >+e e# &!og!"," &+e." '!e"! #" 6.'-? A - #"

6.'-? 6.'-? B e E='e# ,e.i"te #" o&'i/ 2ork#eet# e%&e'i)i'",o% #"% )i#"% - 'o#+,"% e #" >+e .ebe i! #" ,"t!i0 !e%&e'tiv",ete6 P"!o &"!" e##o .ebe,o% t!"b"j"! 'o #"% v"!i"b#e% , %,



















A227 5& /. $.5&-.: Co e# '/.igo >+e &!e%et",o% " 'oti+"'i/ &o.!e,o% ob%e!v"! '/,o %e "''io" #" v"!i"b v"!i"b#e #e flag ( b".e!" ##","." "%( -" >+e o% )"'i#it" " +" i)ii.". .e o&'ioe% e i%t!+''ioe% "# "'tiv"!#" ) I) 8)#"g  29 T?e M%gBo= 8ERROR9 M%gBo= 8P"!" #" %+," !e%t" o .ivi%i/ .e ,"t!i'e% @ C?!8249 @ Debe tee! e# ,i%,o +,e!o .e )i#"% - 'o#+,"% @ C?!8249 @ E% .e'i! ,i%," .i,e%i/9





















L" v"!i"b#e flag 8b".e!"9 i)o!," "# +%+"!io "'e!'" .e #"% !e%t!i''ioe% >+e tiee% #"% o&e!"'ioe% 'o ,"t!i'e% 'o,o e% e# '"%o .e 'oi'i.e'i" e e# 1,e!o .e )i#"% - 'o#+,"% e #" %+," !e%t" - .ivi%i/ o e #" ,+#ti&#i'"'i/ i)o!," "# +%+"!io .e >+e e# 1,e!o .e





















C





















.6 E% + #e #eg+ g+"j "jee &o! &o!t" t"b# b#ee E%te #eg+"je &e!,ite +ti#i0"! e# ,i%,o '/.igo e .i)e!ete% e>+i&o% - %i%te,"% i)o!,;ti'o% /%e" >+e e% i.e&e.iete .e "!>+ite't+!" .e '+"#>+ie! ,;>+i"6 e6 E% + #eg #eg+"j +"jee !e#"ti !e#"tiv", v",et etee &e>+e &e>+eoo E%te e% + #eg+"je e'o/,i'o e '+"to " e=&!e%ioe% %e !e)ie!e %e &+e.e .e%'!ibi! e &o'o e%&"'io e% );'i# - !;&i.o .e "&!e.e!6 )6 Tiee Tiee "b+ "b+."' ."'i" i" .e .e o&e!". o&e!".o!e% o!e% - ti&o% ti&o% .e ."to% ."to% E%te E%te #eg #eg+" +"je je &!;' &!;'ti ti'" '",e ,et tee &o%e &o%eee + o&e! o&e!". ".o! o! &"!" &"!" '"." '"." +" +" .e #"% #"% &o%i &o%ib# b#e% e% o&e!"'ioe% e '/.igo .e ,;>+i"6 To.o &!og!"," e C .e + o ,;% )+'ioe%6 L" )+'i/ >+e %e eje'+t" .e &!i,e! e%





















E% +%+"# >+e e + &!og!"," e# +%+"!io it!o.+0'" ."to% &o! te'#".o 6&"!" e##o 'ot",o% 'o v"!i"% &o%ibi#i.".e%$ +%"! #"% )+'ioe% .e #" bib#iote'" e%t;."! e% #o ,;% 'o?e!ete6 /canf

A# +ti#i0"! #" &"#"b!" %'") o%ot!o% &o.e,o% ?"'e! >+e e# +%+"!io it!o.+0'" ."to% &o! te'#".o6 E# +%o .e %'") e% .e #" %ig+iete ,"e!"$ %'")8Q.+,9 %'")8Q.+,9 e%t" 1#ti," e=&!e%i/ i.i'" "# &!og!",".o! >+e .ebe %o#i'it"! + +,e!o ete!o6 printf

E# +%o .e# &!it) e% %i,i#"! "# .e %'") #o >+e ?"'e e% #ee! +" v"!i"b#e% &!it) #o ?"'e &"!" i,&!i,i!#"6 De e%t" ,"e!" &o.e,o% i,&!i,i! e &"t"##" -" %e" + ,e%"je o e# v"#o! 'otei.o e +" v"!i"b#e6 L" %it"=i% .e# &!it) e% "%($ &!it) 8Q. +,9 e%t" %ete'i"





















De e%te ,o.o e# +%+"!io &o.!; it!o.+'i! e #"% .o% v"!i"b#e% #o% v"#o!e% >+e e# .e%ee - >+e e%t< .e "'+e!.o 'o e# ,e%"je >+e i.i'" e# &!og!","$ "Ingre#e el n$mero %e fila# %e la matriz A 4 B", e "Ingre#e el n$mero %e columna# %e la matriz A 4 B" 6























Co.i'i/$ %i #" '+,&#e eje'+t"!" #" "''i/ o "''ioe% e i'!e,eto o .e'!e,eto #" v"!i"b#e .e 'ot!o# %io #" '+,&#e #" 'o.i'i/ %e %"#e .e# 'i'#o6 I'!e,eto$ >+e &+e.e %e! &o%itivo o eg"tivo 8.e'!e,eto96

I-&0* 5& /.0 6.'-2&0 A 9 B E e%te ,o,eto 'o,o -" tee,o% ig!e%"."% #"% )i#"% - 'o#+,"% >+e e%t; 'o,o





























































#o% ,i%,o &"!" e# for .e .e j e# '+"# e% numfa !e'o!!e e# ,i%,o 'i'#o .e# for 6 A# )i"# .et!o .e# if - .e #o% 3 for !e"#i0",o% !e"#i0",o% #" %+,"6

E e# '"%o el#e %i i e% ig+"# ig+"# " +o +o - numfa e% ,eo! o ig+"# eto'e% tee,o% >+e #" ,"t!i0 v" " .e'i! e!!o! - flag v" v" ?"'e! ig+"# " +o e# '+"# %e!; e=&#i'".o ,;% ".e#"te 6





















E/ 2.0& ! 5&/ 6& Re"#i0",o% #o ,i%,o >+e ?i'i,o% e e# '"%o 2  e e%te '"%o #o 1i'o >+e '",bi" e% #" !e%t" .et!o .e #o% 3 4*-6























E e# '"%o el#e %i i e% ig+"# ig+"# " +o +o - numfa e% ,eo! o ig+"# eto'e% tee,o% >+e #"









































C+".o 4/. e% ig+"# " 3 v" " ,o%t!"! #o %ig+iete$ P"!" !e"#i0"! #" ,+#ti&#i'"'i/ .e





























































































































































































































































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