205sp11-practice-exam2b-solutions

# 205sp11-practice-exam2b-solutions - A5GACCE 4:EXA#B h...

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Unformatted text preview: A5GACCE 4 :EXA#B h e×eÔ ÖÓb ÐeÑ ×ÖeÔ Öe×eÒ ØØh eØÝÔ e×Ó fÕÙ e×Ø iÓÒ ×ÝÓÙÑ igh ØÒdÓÒ Øh e×eÓÒd4 :eÜaÑ iÒ Øh i× ×eÑ e×Øe Ö×a Øh5h eÝa ÖeØak eÒd iÖeØ ÐÝ fÖÓÑ Ó Ðd eÜaÑ ×h eb e×ØÛ aÝ ØÓÙ ×eØh i×ÖeÚ ieÛ i× ØÓÔ Öe ØeÒd Øha ØeahÓ fØh e×eÔ ÖaØ ieeÜaÑ ×a ÖeØh eÖea ÐØh iÒgaÒd Øak eØh eeÜaÑÛ iØhÓÙ Øae×× ØÓÒÓ Øe×Ó ÖØh eØeÜ ØÓ ÖaÒÝÓ Øh e Öh e ÐÔh eÒÙ × iÒgÝÓÙ ÖÒÓ Øe×aÒd ØeÜ Øg Öad eÝÓÙ ÖØÖ ia ÐeÜaÑ A Ò ×Û e Ö×Û iÐÐb eÑ ad eaÚa iÐab ÐeÙ e×daÝÓÒ Øh eÛ ebÔage F Ó ÖØh eÑ a ØÖ iÜ A = 1 2 3 2 3 1 1 5 , Òdaba × i× fÓ ÖØh eÚ eØÓ Ö×ÔaeÓ fÚ eØÓ Ö× X = x 1 x 2 x 3 ×Ó Øha Ø AX = 0 Ó ÐÙ Ø iÓÒ :: F iÖ×ØÖÓÛ ÖedÙe : A = 1 2 3 2 3 1 1 5 = ⇒ 1 2 3 − 1 − 5 1 5 = ⇒ 1 2 3 1 5 = ⇒ 1 − 7 1 5 . h eÒÒÓ Øe× iÒeØh eÖaÒk i× aÒd Øh ed iÑ eÒ × iÓÒÓ fØh e×ÔaeÓ fa ÐÐ×Ùh X i× Øh eÒ Øh e×Ó ÐÙ Ø iÓÒ ×Ôae i×d iÑ eÒ × iÓÒa Ðak e x 3 = 1 ØÓÒd x 1 aÒd x 2 : x 1 = 7 x 2 = − 5 aÒd ×Ó 7 − 5 1 i×aba × i×fÓ ÖØh e×Ó ÐÙ Ø iÓÒ ×ÔaeiÒeØh i×Û a ×Öea ÐÐÝaÒÙ ÐÐ×ÔaeÓ faÑ a ØÖ iÜ iØ ×Ó ÖØÓ fhad ØÓb eÛ Ö iØØeÒ iÒ Øe ÖÑ ×Ó fÓ ÐÙÑ ÒÚ eØÓ Ö× F iÒdba ×e× fÓ ÖØh eÖÓÛ ×ÔaeÓ ÐÙÑ Ò ×ÔaeaÒdÒÙ ÐÐ×ÔaeÓ fØh eÑ a ØÖ iÜ A g iÚ eÒbÝ A = 1 2 − 1 3 1 − 1 2 − 2 1 5 − 4 8 Ó ÐÙ Ø iÓÒ : F iÖ×ØØÓÒd Øh eÖÓÛ ×Ôae ØÓÒdaba × i× fÓ Ö iØ ÖÓÛ ÖedÙe 1 2 − 1 3 1 − 1 2 − 2 1 5 − 4 8 = ⇒ 1 2 − 1 3 − 3 3 − 5 3 − 3 5 = ⇒ 1 2 − 1 3 1 − 1 5 3 = ⇒ 1 1 − 1 3 1 − 1 5 3 . A5GACCE 4 :EXA#B h eÖÓÛ ×ÔaeØh eÒ i×ØÛ Ód iÑ eÒ × iÓÒa ÐÛ iØhba × i× braceleftbigbracketleftbig 1 1 − 1 3 bracketrightbig , bracketleftbig 1 − 1 5 3 bracketrightbigbracerightbig . ÓÒd Øh eÓ ÐÙÑ Ò ×ÔaeÛ eÖea ÐÐÝ ×hÓÙ ÐdÓ ÐÙÑ Ò ÖedÙeB Ù ØÛ ekÒÓÛ Øha ØØh e Ó ÐÙÑ Ò ×Ôaeha ×Øh e×aÑ ed iÑ eÒ × iÓÒa ×Øh eÖÓÛ ×Ôae ×Óa ÐÐÛ eÒ eeda ÖeØÛ Ó ÐiÒ ea Ö ÐÝ iÒd eÔ eÒd eÒ ØÚ eØÓ Ö× Û Ó Ú eØÓ Ö×a Öe ÐiÒ ea Ö ÐÝ iÒd eÔ eÒd eÒ ØÛ h eÒÓÒ e i×ÒÓ Ø aÑ Ù ÐØ iÔ ÐeÓ fØh eÓ Øh e Ö×ÓÛ eaÒb e iÒg ÐeÚ e ÖjÙ ×Øg Öab ØÛ ÓÓ ÐÙÑ Ò ×Øha Øa ÖeÒÓ Ø Ñ Ù ÐØ iÔ Ðe×Ó feahÓ Øh e ÖaÒdb edÓÒ eÛ iØh iØhÙ ×aba × i× fÓ ÖØh eÓ ÐÙÑ Ò ×Ôae i× 1 1 1 , 2 − 1 5 .....
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