205f05-final

# 205f05-final - A5FA5FAEXA F iÒd a ÐÐ ×Ó ÐÙ Ø iÓÒ ×Ó fØh e×Ý ×ØeÑ ×Ó feÕÙa Ø iÓÒ × ÔÓ iÒ Ø×Ô eÖÔa Ö Ø a x 1 x 2

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Unformatted text preview: A5FA5FAEXA F iÒd a ÐÐ ×Ó ÐÙ Ø iÓÒ ×Ó fØh e×Ý ×ØeÑ ×Ó feÕÙa Ø iÓÒ × : ÔÓ iÒ Ø×Ô eÖÔa Ö Ø a x 1 + x 2 + x 3 = 1 x 1 + 2 x 3 = 2 x 1 + 2 x 2- x 3 = 3 b 2 x 1 + x 2- 8 x 3- 3 x 4 = 0 3 x 1- 2 x 2- 5 x 3- x 4 = 0 5 x 1- 8 x 2 + x 3 + 3 x 4 = 0 F iÒd Øh ed e Øe ÖÑ iÒaÒ Ø×Ó fØh e fÓ ÐÐÓÛ iÒgÑ a ØÖ ie× 5ÔÓ iÒ Ø×Ô eÖÔa Ö Ø a 2- 1 2 3 5 4 b 2 1 0 0 1 3 0 0 0 0 1 1 0 0 1 2 . F iÒd Øh e iÒÚ e Ö×eÓ fØh eÑ a ØÖ ie× : 5ÔÓ iÒ Ø×Ô eÖÔa Ö Ø a bracketleftbigg 2 2 4 3 bracketrightbigg . b 1 2 2 2 1 0 0 1 0 . 4 5ÔÓ iÒ Ø×Ô eÖÔa Ö Ø a ha ØÓÒd iØ iÓÒ ×Ò eed ØÓhÓ Ðd iÒÓ Öd e ÖfÓ Öa×Ùb ×e Ø S Ó faÚ eØÓ Ö×Ôae V ØÓb ea Ú eØÓ Ö×Ùb ×Ôae? b hÓÛ Øha ØØh e×e Ø S Ó fa ÐÐ 2 × 2 Ñ a ØÖ ie×Û iØhd e Øe ÖÑ iÒaÒ Øi× ÒÓ Ø aÚ eØÓ Ö×Ùb ×Ôae Ó fØh e×Ôae V Ó fa ÐÐ 2 × 2 Ñ a ØÖ ie×[iÒ Ø :Ó×hÓÛ iØ i×ÒÓ Øa×Ùb ×ÔaeÝÓÙÓÒ ÐÝ Ò eed ØÓ×hÓÛ Øha ØÓÒ eÓ fØh eÓÒd iØ iÓÒ ×fÖÓÑ Ôa ÖØ a dÓe×ÒÓ ØhÓ Ðd fÓ Ö×ÓÑ ehÓ ie Ó fe ÐeÑ eÒ Ø×Ó f S ℄ 5 Ó ÐÚ eØh e fÓ ÐÐÓÛ iÒgd ie ÖeÒ Ø...
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## This note was uploaded on 10/03/2011 for the course MATH 205 taught by Professor Zhang during the Spring '08 term at Lehigh University .

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205f05-final - A5FA5FAEXA F iÒd a ÐÐ ×Ó ÐÙ Ø iÓÒ ×Ó fØh e×Ý ×ØeÑ ×Ó feÕÙa Ø iÓÒ × ÔÓ iÒ Ø×Ô eÖÔa Ö Ø a x 1 x 2

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