高等代數(shù)二次型習(xí)題精解

1、第八章第八章二次型二次型習(xí)題精解習(xí)題精解1（Ⅰ）用非退化線性替換化下列二次型為標(biāo)準(zhǔn)形，并利用矩陣驗算所得結(jié)果：1）323121224xxxxxx???2）23322221214422xxxxxxx????3）32312122216223xxxxxxxx????4）423243418228xxxxxxxx???5）434232413121xxxxxxxxxxxx?????6）4342324131212422212222442xxxxxxx

2、xxxxxxxx????????7）43322124232221222xxxxxxxxxx??????解1）已知??323121321224xxxxxxxxxf????先作非退化線性替換（1）??????????33212211yxyyxyyx則??312221321444yyyyxxxf????2223233121444yyyyyy????????222333142yyyy?????再作非退化線性替換（2）???????????332

3、23112121zyzyzzy則原二次型的標(biāo)準(zhǔn)形為??2322213214zzzxxxf?????????????????100210211T且有???????????????????????????????????????????????000010001100210211420221011122011001ATT（3）已知??32312122213216223xxxxxxxxxxxf?????由配方法可得??????23322223

4、223231212132144222xxxxxxxxxxxxxxxxf?????????????23223212xxxxx?????于是可令???????????3332232112xyxxyxxxy則原二次型的標(biāo)準(zhǔn)形為??2221321yyxxxf??且非退化線性替換為???????????????33322321121212321yxyyxyyyx相應(yīng)的替換矩陣為???????????????????1002121023211T且有