工程数学线性代数课后习题答案 - 图文

?4??x1??3??x???3? ?2??k?4?(k为任意常数)

?x3????x4??3??1???x1?2x2?x3?x4?0 (2)?3x1?6x2?x3?3x4?0??5x1?10x2?x3?5x4?0

有

解 对系数矩阵A进行初等行变换 A?121?1??120?1??36?1?3?~?0010??5101?5??0000?????

?x1??2x2?x4?x?x于是 ?22x3?0?x?x?44故方程组的解为

?x1???2??1??x??1??0?2 ???k1???k2??(k1

00?x3??0??1????x4??? k2为任意常数)

?2x1?3x2?x3?5x4?0?3x?x?2x3?7x4?0 (3)?124x1?x2?3x3?6x4?0?x?2x?4x?7x?0?1234

有

解 对系数矩阵A进行初等行变换 A?23?31?41?1?2??15??12?7?~?0?36??0?04?7???010000100?0?0?1???x1?0?x?0于是 ?2x3?0?x?0?4故方程组的解为 ?x1?0?x?0 ?2x3?0?x?0?4

?3x1?4x2?5x3?7x4?0?2x?3x2?3x3?2x4?0 (4)?14x1?11x2?13x3?16x4?0?7x?2x?x?3x?0?1234?17???2?~?016???03????0

有 13?17?20??17?00?? 解 对系数矩阵A进行初等行变换

A?34?5?2?33?411?13?7?21?0?3171?19170000

?x?3x?13x?1173174?1920于是 ?x2?x3?x41717?x?x?x3?x3?44故方程组的解为