Lecture 6 (2x2) - %[email protected]:1"[email protected]>1)41...

Info icon This preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: %[email protected]:1 "1/@A>1 )41 8;35/ ;2 %<1: //1?? %>01>? % %? %$ M8B->; "- &->>- &N>1F *# :@>;0A/@5;: ;99;: /4->-/@1>[email protected]/? @; % % (@[email protected] ;2 % % (@[email protected]/ (@[email protected] E:-95/ (@[email protected] -:A->E % % [email protected] C;>7 ;:/8A?5;:? M 8B->; "- &->>- &N>1F *# /;: "1/@A>1 M8B->; "- &->>- &N>1F *# /;: "1/@A>1 :@>;0A/@5;: :@>;0A/@5;: (-91 /1:@>-8 /;:/1>: @4-: 5: " % /;:@>;885:3 B5;81:/1 :[email protected] ;2 /;:@>;885:3 B5;81:/1 A?5:3 1/;:;95/ >1:@? -? [email protected] C-? @41 /-?1 2;> " %? 5: % % C1 ->1 5: - B5>@A-8 /5>/81 85:75:3 ;<1: -//1?? -:0 /;:@>;8 ;2 B5;81:/1 :@1>>[email protected];:?45<? [email protected]: 019;/>-/E -:0 9->[email protected]? 1/;:;95/ -:0 <;[email protected]/-8 ?<41>1 [email protected] >15:2;>/1 1-/4 ;@41> 19;/>-/E %<1: //1?? #->[email protected]? )41>1 ->1 ?;91 59<;>@-:@ 18191:@? [email protected]:5:3 @41 [email protected] >15:2;>/5:3 1=A585.>5A9 5: % %? 19<4-?5F5:3 [email protected] [email protected]:10 .E 5:[email protected]@[email protected];:? -:0 <;85/51? 8571 A:5B1>?-8 10A/[email protected];: -:0 <>;B5?5;: ;2 <A.85/ 3;;0? &;[email protected]/-8 <->@51? /;:@>;8810 .E /;9<[email protected]@5B1 181/@5;:? ;<1: -//1?? 5: <;[email protected]/? ;9<[email protected]@5B1 ;<1: -//1?? 9->[email protected]? 81-05:3 @; /;[email protected]? 5: >1:@ ?1175:3 <->@51? @4>;A34 1/;:;95/ 91/4-:5?9? [email protected]>5;>[email protected];: 5: 5:@1>:[email protected];:-8 9->[email protected]? 9;.581 >1?;A>/1? 81-B1 @41 /;A:@>E &;[email protected]/-8 ?/51:/1 -:0 1/;:;95/? @1:0 @; :1381/@ @45? 59<;>@-:@ 2-/@ $1C /;:/1<@ ;2 019;/>-/E :;@ >[email protected]>5/@10 @; @41 ?411> 2-/@ ;2 4-B5:3 181/@5;:? M8B->; "- &->>- &N>1F *# /;: "1/@A>1 M 8B->; "- &->>- &N>1F *# /;: "1/@A>1 ;99;: /4->-/@1>[email protected]/? @; % %? ;?1<4 (/4A9<[email protected]> ;;>[email protected]< /;:[email protected];: C1 C588 [email protected] @45? 5: @41 :[email protected] 81/@A>1? <1><[email protected] 85B10 [email protected]@1 -:0 /;:?;[email protected] /;:@>;8 ;B1> B5;81:/1 ,5018E 4180 [email protected] ;2 .18512? 5: [email protected] 2;> -88 /[email protected]:? '[email protected] [email protected] .1 5: 85:1 [email protected] @41?1 .18512? ?A<<;>@5:3 @41 1=A585.>5A9 >11 1:@>E 5:@; 1/;:;95/ <;[email protected]/-8 >18535;A? -:0 10A/-[email protected];:-8 -/@[email protected]? (A<<;>@ 2;> ;>3-:[email protected];:-8 2;>9? 5: 1-/4 -/@[email protected] ;<1: @; -88 9<->@5-8 1:2;>/191:@ ;2 >A81 ;2 8-C 2;> -88 /[email protected]:? 9<1>?;:-8 1D/4-:31 M8B->; "- &->>- &N>1F *# /;: "1/@A>1 M 8B->; "- &->>- &N>1F *# /;: "1/@A>1 ;99;: /4->-/@1>[email protected]/? @; % %? ? C1 C588 ?11 <;5:@? -:0 ->1 @41 1??1:/1 ;2 % % %>3-:[email protected];:? ->1 @41 8521.8;;0 ;2 .;@4 <;[email protected]/-8 -:0 1/;:;95/ /;9<[email protected]@5;: -:0 5: % % @41 -//1?? @; @41?1 ;>3-:[email protected];:? 5? 3A->-:@110 @; 1B1>E;.0E ;: -: 1=A-8 -:0 2>11 .-?5? )41E ->1 /8;?18E 85:710 @; @41 (/4A9<[email protected]>5-: 501- ;2 />[email protected] [email protected]>A/@5;: C45/4 5? ?11: -? @41 9-5: 91/4-:5?9 2;> 1/;:;95/ /4-:31 -:0 <>;3>1?? )45? />[email protected] [email protected]>A/@5;: 5? :;@ <;??5.81 ;> [email protected] 5? @41 ?;A>/1 ;2 3>[email protected] 5:[email protected]@E 5: " %? .1/-A?1 [email protected] @4>[email protected]:? @41 1=A585.>5A9 >1-/410 @; /;:@>;8 B5;81:/1 &;5:@? -:0 [email protected]>1?? @41 59<;>@-:/1 ;2 - 71E 18191:@ 5: @41 191>31:/1 ;2 % % 59<1>?;:[email protected] ,1 C588 ?11 @[email protected] <;5:@ [email protected]:/1 ;2 /;:[email protected]:@ .18512? /-: .1 /;:?501>10 -? - .E<>;0A/@ ;2 @41 % % [email protected]?182 : @41 :[email protected] /8-??1? C1 C588 <>;B501 -: 1D<8-:[email protected];: ;2 4;C 59<1>?;:[email protected] -:0 @41 2>11 -//1?? @; ;>3-:[email protected];:? 191>31? )45? 5? 71E 18191:@ 5: ;A> [email protected];>E [email protected] 2;> @41 9;91:@ @-71 @419 -? 35B1: M8B->; "- &->>- &N>1F *# /;: "1/@A>1 ;99;: /4->-/@1>[email protected]/? @; % %? ? ?11: 5: @41 5:@>;0A/@5;: - G:-8 /;99;: /4->-/@1>[email protected]/? ;2 % % ;> >5/41> /;A:@>51? 5? @415> .5331> 3;B1>:91:@ )41>1 ->1 [email protected] [email protected] @4>11 >1-?;:? @; @45? &>;B5?5;: ;2 ?;/5-8 5:?A>-:/1 <>;3>-9? @; 8;C1> @41 /;[email protected] 5: 9->[email protected] <->@5/5<[email protected];: 1 3 A:19<8;E91:@ 5:?A>-:/1 -:0 @4A? >10A/1 @41 <>;[email protected] ;2 -: -:@59->[email protected] <;[email protected]/-8 >1-/@5;: 0A>5:3 .-0 @591? 9<1>?;:[email protected] 81-0? @; 3>[email protected]> 3;B1>:91:@ .1/-A?1 [email protected] -88;C? @41 <>;B5?5;: ;2 - C501> >-:31 ;2 <A.85/ 3;;0? -:0 ?1>B5/1? (@[email protected] .A5805:3 @41 [email protected]@1 :110? @; <>;B501 ?;91 <A.85/ 3;;0? -:0 ?1>B5/1? @; [email protected]: % % M8B->; "- &->>- &N>1F *# /;: "1/@A>1 (@[email protected] ;2 % %? ;>/1? ;2 [email protected]@5/ [email protected]@E 5: % %? )41 G>[email protected] 18191:@ 1:?A>5:3 [email protected]@5/ [email protected]@E 5? [email protected]: /;9<[email protected]@5;: -? - 91-:? @; )C; ?;A>/1? ;2 [email protected]@E [email protected] .1 2-/10 (@[email protected]/ [email protected]@E />[email protected];: ;2 ?182 1:2;>/5:3 ;<1: -//1?? ;>01> <>1B1:@5:3 @; 013>-01 5:@; - :[email protected]>-8 [email protected]@1 E:-95/ [email protected]@E 4;C 0; % %? 2-/1 -: 1B1> /4-:35:3 -:0 A:/1>@-5: C;>80 '1919.1> @[email protected] @45? 5? - 9-6;> ?;A>/1 ;2 5:[email protected]@E 5: " %? .1/-A?1 @41 1/;:;95/ >1:@? [email protected]:5:3 @41 0;95:-:@ /;[email protected];: /;A80 .1 ?1>5;A?8E -L1/@10 .E @41 <>;/1?? ;2 />[email protected] [email protected]>A/@5;: ;> @41 <>;/1?? ;2 ?;/5-8 -:0 1/;:;95/ /4-:31 :/1:@5B1? @; ;<<;[email protected];: <->@51? @; /;:/15B1 9;>1 1K/51:@ C-E? @; 01-8 [email protected] <>;.819? 5: ;>01> @; 5:/>1-?1 @415> /4-:/1? ;2 C5::5:3 181/@5;:? $110 ;2 9;01>[email protected];: 5: <;85/51? :;@ @; 8;?1 /4-5> >1:@ ?1175:3 <;85/51? 2-B;>5:3 - 95:;>[email protected] <>;.-.8E >10A/1? @41 8571854;;0 ;2 >1 181/@5;: ;9<[email protected]@5;: [email protected]: <->@51? 05?/5<85:1? -:0 2;[email protected]>? ;>3-:[email protected];: [email protected]: <->@51? )45? 5? 59<;>@-:@ @; -B;50 2-/@5;:-8 [email protected]? 1 3 05?5:@13>[email protected];: ;2 @41 1L1>?;:5-: &->@E 5: [email protected]<81 2-/@5;:? C41: @41 101>[email protected] &->@E 05?-<<1->10 [email protected]: -:0 :0;31:;A? <8A>[email protected] -<<>;-/4 )4>[email protected] ;2 1:@>E 9;01>[email protected] >1:@ ?1171>?H <;85/E 019-:0? :1K/51:@ <;85/51? A:01>95:1? @41 @-D .-?1 2;> @41 3;B1>:91:@ -:0 @41: [email protected]? @41 5:/A9.1:@H? /;[email protected];: M8B->; "- &->>- &N>1F *# /;: "1/@A>1 M8B->; "- &->>- &N>1F *# /;: "1/@A>1 ;>/1? ;2 [email protected]@5/ [email protected]@E 5: % %? ;>/1? ;2 [email protected]@5/ [email protected]@E 5: % %? <>;B501? @41 ?1/;:0 18191:@ 1:?A>5:3 [email protected]@5/ [email protected]@E 5: % %? $,, <;5:@ @; @4>11 9-5: /4-::18? &>5/1 91/4-:5?9 2-/[email protected]@1? <8A>-85?9 -:0 <->@E /;9<[email protected]@5;: &>5/1? /;;>05:[email protected] -31:@? -:0 ?<>1-0 5:2;>[email protected];: ;: @41 59<-/@ ;2 <;85/51? -E17 $;>@4 )41 3-5:? ;2 @41 9->[email protected] /-: .1 ?4->10 1 3 5:/>1-?1 5: <>;0A/@[email protected] 81-05:3 @; 45341> C-31? 5: @41 1/;:;9E )45? /-: .1 <>;[email protected]/ C41: 2-/5:3 - 38;.-8 ;<1: -//1?? 2>;9 @41 1/;:;95/ <;5:@ ;2 B51C ';81 ;2 5:@1>:[email protected];:-8 /;9<[email protected]@5;: -9;:3 ;<1: -//1?? ;>01>? '1:@ />[email protected];: <;85/51? /-: 0-9-31 5:@1>:[email protected];:-8 /;9<[email protected]@5B1:1?? ?<1/5-88E @>A1 2;> ?9-88 @>-05:3 /;A:@>51? +5;81:/1 -:0 C-> :110 @; ?A>B5B1 C41: 2-/5:3 [email protected]>:-8 @4>[email protected]? [email protected]:3 2>;9 I-33>1??5B1 <;C1>2A8 :[email protected]>-8 [email protected]@1?J #;01>[email protected];: ;2 <;85/51? -:0 <>;9;@5;: ;2 5:@1>:[email protected];:-8 /;;<1>[email protected];: 1 3 ;80 ,-> $ )% #->?4-88 &8-: -:0 @41 % 0B-:@-31 @; 0>-C >1?;A>/1? 2>;9 @41 1/;:;9E 0A>5:3 C-> @591? #;>1 <>;0A/@5B1 1/;:;9E .>;-01> @-D .-?1 >[email protected]> [email protected] @; .;>>;C .E >-5?5:3 .;:0? -:0 @4A? [email protected]>[email protected] @41 1/;:;95/ .A>01: ;B1> - 8;:31> <1>5;0 ;2 @591 M8B->; "- &->>- &N>1F *# /;: "1/@A>1 M8B->; "- &->>- &N>1F *# /;: "1/@A>1 ;>/1? ;2 [email protected]@5/ [email protected]@E 5: % %? E:-95/ [email protected]@E >1=A5>1? @41 [email protected] @; /;<1 [email protected] :1C <>;.819? -:0 [email protected]/ 05?8;/[email protected];:? %<1: //1?? %>01>? /;A:@ ;: @C; -0B-:@-31? [email protected] >1?<1/@ @; " % @; 2-/1 -: 1B1> /4-:35:3 C;>80 % %? 4-B1 - .>;-01> .-?1 ;2 5:05B50A-8? 01-85:3 [email protected] /A>>1:@ <>;.819? @4-:7? @; ;<1: -//1?? @; ;>3-:[email protected];:? -:0 3>[email protected]> 5:/1:@5B1? @; 8;;7 2;> ?;[email protected];:? @; @41 <>;.819? @[email protected] 9-E ->5?1 5: @41 <;[email protected]/-8 -:0 1/;:;95/ ->1:%<<;[email protected];: <->@51? 8;;75:3 2;> [email protected]@>-/@5B1 <>;<;?-8? -:0 ?;[email protected];:? 2-/[email protected]@5:3 B5/@;>E 5: @41 :[email protected] 181/@5;:? :@>1<>1:1A>? 8;;75:3 2;> 5::;[email protected];:? ;<1:5:3 - :5/41 5: @41 9->[email protected] % % [email protected] C;>7 (5958-> 5:[email protected]@[email protected];:? E5180 B1>E 05L1>1:@ >[email protected]? 5: -: % % @4-: 5: " % //;>05:3 @; [email protected] C1 4-B1 ?11: ?; 2-> @41>1 ->1 [email protected] [email protected] @4>11 >1-?;:? @; @45? )41 ;<1: -//1?? -:0 /;9<[email protected]@5B1 91/4-:5?9? 5? ?4;>@ /5>/[email protected] ,1-71> /5B58 ?;/[email protected] 5: " %? .1/-A?1 ;2 @41 5:[email protected] ;2 -88 @41 /[email protected]:? @; 2;>9 -: ;>3-:[email protected];: 1 3 <;[email protected]/-8 <->@E ;> G>9 >1919.1> 2;> 1D-9<81 @41 /-?1 ;2 [email protected]/? /;991:@10 5: /8-?? [email protected] E;A /-: -8?; @45:7 ;2 @;0-EH? 'A??5- (A0-: $;>@4 !;>1"1?? >185-:/1 ;: @-D1? 1/;:;95/ >1:@? 5? @41 38A1 ;2 ?;/[email protected] ?; 9-D595F5:3 @41 ?5F1 ;2 @41 <51 5? :;@ @41 <>59->E /;:/1>: :[email protected] @; -88;/[email protected] .1:[email protected]? -//;>05:3 @; 59<1>?;:-8 />[email protected]>5;>3-:[email protected];:? 5: " % ->1 -: 59<;>@-:@ <->@ ;2 @41 [email protected]>A/@A>1 ;2 <>5B58131 711<5:3 @41 1=A585.>5A9 5: @41 0;95:-:@ /;[email protected];: >[email protected]> [email protected] @; <>;B501 />105.81 /;[email protected]:@? : " %? 9->[email protected]? 0; :;@ C;>7 -//;>05:3 @; @41 ;<1: -//1?? 8;35/ >1:@? ->1 />A/5-8 -:0 @41E 8-/7 @41 (/4A9<[email protected]>5-: /4->-/@1> -/@A-88E -? [email protected]@10 -.;B1 />[email protected] [email protected]>A/@5;: 5? -: 59<;>@-:@ ?;A>/1 ;2 5:[email protected]@E 5: " %? M 8B->; "- &->>- &N>1F *# /;: "1/@A>1 M8B->; "- &->>- &N>1F *# /;: "1/@A>1 % % [email protected] C;>7 @1:@[email protected] ?A99->E 18512? -88 @41 <>1B5;A? 2-/@? 81-0 @; @41 5:[email protected] ;2 " %? @; <>;B501 <;85/51? @[email protected] ?4->1 @41 3-5:? ;2 1/;:;95/ 3>;[email protected] 88 [email protected] C1 4-B1 ?11: :[email protected]>-88E 81-0? @; - :1C /;:?501>[email protected];: ;2 @C; 59<;>@-:@ /;:/1<@? 019;/>-/E -:0 >[email protected]>[email protected];: )41 /;:/1<@ ;2 019;/>-/E [email protected] 3; C188 .1E;:0 @41 /181.>[email protected];: ;2 181/@5;:? )41>1 [email protected] .1 ;<1: -//1?? 59<1>?;:[email protected] 5:/8A?5;: -:0 [email protected] 5: ;>01> @; [email protected] -88 @41 .1:[email protected]? 5:B;8B10 5: -: % % &A.85/ 3;;0? -:0 ?1>B5/1? -? /;9<8191:@->E -:0 :;@ F1>; ?A9 3-91 ?;/5-8 019;/>[email protected]/ /;:?1:?A? [email protected]? /-: .1 5:@1>[email protected] 5: <>;9;@5:3 @41?1 019;/>[email protected]@5;: ;2 C182->1 C1 C588 ?11 ?;91 1D-9<81? [email protected]> 5: @41 /;A>?1 M 8B->; "- &->>- &N>1F *# /;: "1/@A>1 M8B->; "- &->>- &N>1F *# /;: "1/@A>1 @1:@[email protected] ?A99->E )41 <>1B5;A? ?/4191 ?4;C? 4;C @41 <;[email protected]/-8 -:0 @41 1/;:;95/ [email protected] [email protected] >15:2;>/1 1-/4 ;@41> )41 .;;7 ?119? @; [email protected] -: 59<85/[email protected] <>1??A>1 ;2 9->[email protected]? ;: @41 <;85/51? -0;<@10 .E 3;B1>:91:@ C41: ?-E5:3 52 <;[email protected]/-8 -/@;>? -:@5/5<[email protected] @41 <;@1:@5-8 >1-/@5;:? ;2 1/;:;95/ -/@;>? @45? [email protected]>? @41 @E<1? ;2 <;85/51? @[email protected] C;A80 /-A?1 1/;:;95/ -/@;>? @; .1/;91 <;[email protected]/-88E -/@5B1 )45? 5? ?5958-> @; @41 >1-?;:5:3 01B18;<10 .E ;: [email protected]> 18?1C41>1 % % '*# "'& " &' #%! $#* % '# ##& !#" ' & ' %" ' ) & !, ) ' $#* % + ( &#! # ' ' %" ' ) & %#! " #"& % ' " #" ' * # "' $ ' % ' #"& ! , &' " %#! ##& " ", # ' & $# & "#' & % , "#* " '' #& & ' $#* % " ' !#' ) '# ' %#" ! #" &' % " "'%# ( ' #" '# % %+ $ M 8B->; "- &->>- &N>1F *# /;: "1/@A>1 ;:/8A?5;:? % %? /;:@>;8 B5;81:/1 @4>;A34 ;<1: 2>11 59<1>?;:-8 -:0 1=A-8 -//1?? @; 1/;:;95/ -:0 <;[email protected]/-8 ;>3-:[email protected];:? (;91 ;2 @41 /;>>[email protected];:? C1 ;.?1>B10 5: @41 5:@>;0A/@;>E /8-?? >5/41> /;A:@>51? 4-B1 .5331> 3;B1>:91:@? -:0 9;>1 ;>3-:[email protected];?: ->1 [email protected] @41 41->@ ;2 @41 8;35/ ;2 % %? -:0 ->1 /;?1=A1:/1 ;2 @41 :;@5;:? ;2 ;<1: -//1?? -:0 59<1>?;:[email protected] )41 >[email protected] ;2 @41 <>1B5;A? ?/4191 5? - 3>[email protected]> @; /;<1 [email protected] 1B;[email protected];: -:0 :1C <>;.819? M8B->; "- &->>- &N>1F *# /;: "1/@A>1 ...
View Full Document

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern