线性代数知识点归纳与梳理

Dn−1+b(x−a).(1.11)Tn−1T由Dn表达式中a,bé称性,知D=(x−a)Dn−1+a(x−b),而D=D,可n−1Dn=(x−a)Dn−1+a(x−b).(1.12)联立(1.11)和(1.12)式,消去Dn−1a(x−b)n−b(x−a)nD=.na−b典.~K2试证???x−10···00??????0x−1···00????.....?nn−1?.....?=x+a1x+···+an−1x+an.?????000···x−1????anan−1an−2···a2x+a1?y²:){一.设法把主é角线上x变为0,2按1˜?Ð开.???x−10···000??????0x−1···000????......??......?Dn=?????000···x−10????000···0x−1??????anan−1an−2···a3a2x+a1????x−10···000??????0x−1···000????......?cn−1+xcn?......?========?????000···x−10????000···00−1????2??anan−1an−2···a3x+a1x+a2x+a1????x−10···000??????0x−1···000????......?cn−2+xcn−1?......?==========?????000···0−10????000···00−1????332??anan−1an−2···x+a1x+a2x+a3x+a1x+a2x+a1????0−1···00??????00···00????....?cj+xcj−1?....?========?????00···−10????00···0−1????nn−1n−1n−22??x+a1x+···+anx+a1x+···+an−1···x+a1x+a2x+a1