线代习题(1-3章)(2)

??2x?y?z?w?1?x1?2x2?x3?x4?05、求解线性方程组 ① ???4x?2y?2z?w?2 ②??3x1?6x2?x3?3x4?0

????2x?y?z?w?1??5x1?10x2?x3?5x4?0??(2??)x1?2x2?2x3?16、设??2x1?(5??)x2?4x3?2

????2x1?4x2?(5??)x3????1当?取何值时，此方程组有惟一解？无解或有无穷多解？并在有无穷多解时求解.

??a11x1?a12x2?...?a1nxn?b1??a21x1?a22x2?...?a7、证明：如果线性方程组?2nxn?b2????????????????

????????an?11x1?an?12x2?...?an?1nxn?bn?1a11a12...a1nb1有解，则行列式Da21a22...a2nb2n?1?...............?0

an?11an?12...an?1nbn?1??x1?x2?a1??x2?x3?a258、证明：线性方程组??x?3?x4?a3 有解的充要条件是?ai?0.在有解时，求全部解.

i?1??x4?x5?a4??x5?x1?a5??a11x1?a12x2?...?a1nxn?b1??a21x1?a22x2?...?a2nxn?b9、证明：线性方程组?2的系数矩阵????????????????????A?(aij)n?n与矩阵

????an1x1?an2x2?...?annxn?bn??a11a12..a1nb1??a21a22..a2nb?2? C???..........?的秩相等，则此线性方程组有解. ??an1an2..annb?n??b1b2..bn0??

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