05-3 - Žssw WWxŒy —• “’ Œ–”‘   Žssw WWxŒy —• “’ Œ–”‘   v w ™‚y © Œy v w ™‚y © Œy ‚w‚9Œy v ¯ w Ž

Info iconThis 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: Žssw WWxŒy —• “’ Œ–”‘   Žssw WWxŒy —• “’ Œ–”‘   v w ™‚y © Œy v w ™‚y © Œy ‚w‚9Œy v ¯ w Ž w w¡w9Œy ±’¤± zEw° ¨“¦¥¤£ ¡G§¡w™G¢ v ¯ w ‚w‚9Œy ±’¤± zEw° ‹w¡WxŒy ¯Žsw ‹¯Žsw w¡WxŒy •™¡™E ¨¢•‘• •¨¢•‘• ™¡™E ¢¡Š‘ •¦ ¢•¦ ¡Š‘ ‹‚w(Wv v vw ‹ v vw ‚w(Wv y y yw wwlWv ‹wwlWv yw ‹ yw wwlWv y y yw wwlWv s Ž vw Ew(Wv ‹ y yw wwlWv ‹ y yw wwlWv ‡ž¹w„¸´}{ Ÿµ ‡ · | ‡ Ÿµ ‡ · | ž¹w„¸´}{ ®ƒ › | †f¨­ µwžE´`² ‡³| µ‡³| wžE´`² ®ƒ › | †f¨­ Ÿ€ …œ ›| ‚ˆž”¢7š ‰ ‡ …ƒ  € ~ | Šˆ†„‚7}{ ‰ ‡ …ƒ  € ~ | Šˆ†„‚7}{ v™zxWv ysw vysw ™zxWv s zxWv ysw v™zxWv ysw vysw ™zxWv v™zxWv ysw vysw ™zxWv s zxWv ysw s zxWv ysw v ºª s ¶ª s ¶ª vs W«ª ss w«ª ¬Š«ª s y ˜u y ˜u v Bu t™‹ t ™¯ t w t™ t wŽ t© t ™y t wv t Ws  ƒ h p „ pˆ k p p i h m †j pˆ k † ‰ „ †j r(ˆ CEq‘¢† roRn(‘k l‘y¢(tq f e ’ g “d ˜ – ” “ ihfe™—•‚’ d  ‰ˆ † … „ ‘(y‡RIƒ  € x vu s q p i h ‚tywrtrI$g c aY X V T `b`GWUS §¥¥P H § FD) R¨QIBGECBA 86 4 @9753 1 ) '&  # !      20(¢%$"¨  © § ¥£ ¡ ¨¦¤¢ v | =⇒ z + y − 2x = 0 ⇐⇒ z + y = 2x 123x 1 2 2 y 124z 12 3 x −→ 0 0 −1 y − x 00 1 z−x 12 3 x −→ 0 0 −1 y−x 00 0 z−x+y−x CS (AT ) = RS (A) | t c A =⇒ y − 2x = 0 ⇐⇒ 2x − y = 0 111x 2 2 2 y 324z t w€  1 11 x −→ 0 0 0 y − 2x 0 −1 1 z − 3x a ` I W U SQ I bRYXVTRPH |  @ƒ 9  9 „µ ž E"G„DwŠ„µ 0&$Ÿ „"GŸ ƒ … †!5Ct B ‡ œ  €  œ‰‡ ' % # ƒ€ ƒœ  A y + z = 2x µ 1œ œ  7  ƒ Ÿ‡1 œ1€ ' „‚‡ w‰ „w‡  G‡  6 „ w”F”G4 2x − y = 0 |  @ƒ 9  (x, y, z )T (x, y, z )T µ 1œ‰ œ  7‡  ƒ Ÿ‡1 œ1€ ' „‚‡ w7„w‡  8I 6 „ w”5”G4 Ÿ ž†3”2ž 0"G„)wŠ¹ž(&$Ÿ „"GŸ ƒ … †!‚w€  … ® ‡1 œ  €  œ ‰‡µ ' % # ƒ€ ƒœt A= 2 2 2 324 111 œ ¢› © § ¥ £ ¡ f ¨¦¤¢„ d y t   ƒ € …  Ÿœ§ ¹µ "ˆU @ƒ  ”ž©ƒ ¢ ¤ t z1  t G§  0 0 0 000 t7 | 010 0 0 1 000 100 | ƒ‡ ‡ ¡œ A „„‚–' o t §#  3×3 r = 3 =⇒ CS (A) = R3 = RS (A) 100 0 1 0 000 0 0 0 000 t c A 010 r = 0 =⇒ CS (A) = 0 = RS (A) | ƒ‡ ‡ ¡œ A „„‚–' o t Šœ  ƒ „µ R€ … ¬ ¢  3×3 t w€  a ` I W U SQ I bRYXVTRPH % t zœ  r = 0 col(A) = row(A) % t7 r = 1 col(A) = row(A) % t §#  r = 2 col(A) = row(A) % t   r = 3 col(A) = row(A) % % % t w€  t B A t z1  t §  r = 3 col(A) = row(A) % r = 2 col(A) = row(A) r Ÿ ‚€ r = 1 col(A) = row(A) |œ ƒ ‡ … ‚† A ¹„w´' †ƒ  ƒ @ƒ "G   3&Ÿ ”&Ÿ ™w”1 žw4‚€ wUw†ƒ @ž¦w1 G©!´' 7ž   € # ƒ 1 ƒ ‰ Ÿ ‡ œ ® # µ µ ‡ Ÿ ‡ ƒ § Ÿ ‡ § œ ¨ƒ 1 œ  œ Ÿ ‚€ µ   ƒ 9 ¢ƒ  € ¤¹µ "ˆ… €  ƒ A žE£E% 9 ‡ !œ A ”¹‚z w# ¸ž„ UxzRwG­ ƒ ¢œ œ€1  ƒœ œ  7‡ 1€œ µ ‡ ¥ ¦ A § ¦ r = 0 col(A) = row(A) e © § ¥ £ ¨¦¤¡ ¡ 3×3 © xparticular = x 2 , x4 , x6 0 r 0 q 0 p | ”œ A € „‚¡%”¹¦7 œ A ƒµ€‰ œœµ œ# ‚2œ 9 %  œ E¦‚€ §Ÿ s=1 0=1 | x = (x1 , x2 , x3 , x4 , x5 , x6 ) 7 w„”¨ € †ƒ © |‡µœ§  A œ › A ¢‚t c 7 ‡ 9 ¹µ 4‚€ ž ª ‡  œ |Ÿ  ‡ ‡ t ‚‡ ƒ (® 3¹ o w€  a ` I W U SQ I bRYXVTRPH t ¥§ ‚G ‡ C¥ w‡ 9  ¥w‡ ¦ µ€ ‡ µ ¤Ÿ s=1 7 ž% ƒ s=0 | § ® ‡  7ƒ   œ ¢ [email protected] £U ` W ¡  ‡ C‚‡ ƒ (® 3¹%œ †$' w”1 ž„  Ÿ  ‡ œ … ‡ œ  ‡ C‚‡ ƒ (® 3¹%œ †$' w”1 ž„  Ÿ  ‡ œ … ‡ œ  0 h 1 i 00 q v= r s Ÿ ¡€ 0g § ¦ 0d 7 ž% ƒ Ax = v 00 0f 1e 1a | Ax = v § § Ÿ 2­ t B ƒ A Ÿ 2­ w€  ƒt 0 b A= 0 c 00 p œ ¢› © § ¥ £ ¡ f ¨¦¤¢„ f Ÿ ƒ ‡ ƒ1œ  œ  Ÿ ‡ w‡ „&® 3¹€ ”!´' 7ž„E§ G¨ `ª x2 = 0 −1 b , 0 c 0 x4 = −1 x6 = 0 x= p 0 q 0 r 0 d x2 = 0 0 e , −1 f 0 x4 = 0 x6 = −1 g d a 0 0 −1 h e b + x6 + x4 + x2 0 −1 0 i f c −1 0 0 Ž x6 = 0 a Ÿ‡ ¢w†ƒ œ x4 = 0 ¡ x2 = −1 g 0 h 0 i −1  ® ‡ œœ …‡ œ &†3„%„†$' ‚”1 ž ª ...
View Full Document

This note was uploaded on 06/21/2011 for the course CIVIL 1011 taught by Professor Juan during the Spring '11 term at HKU.

Ask a homework question - tutors are online