1.1-1.3练习参考答案
二、1.D?a11a22a33a44???1????1???2143???1243?a11a22a34a43???1???1324?a11a22a33a44???1???2134?a12a21a33a44
a12a21a34a43?abcd?ab?ad?cd?11.4练习参考答案
c2?c1c3?c1c4?c1a00ba2aca?b3a?2bda?b?c4a?3b?2cc3?2c2c4?3c2a?00ba0ca?bada?b?c2a?bc4?3c3a?00ba0ca?bada?b?c2a?b?a4二、1.D?03a6a?4b10a?6b?3c003a7a?3b000a2.从第一行开始，前一行减去后一行0a12?x2a13?a23?a1n?a2n00a23?x3?a2n?a3n按第一列展开nnDn?????????1?n?1x1??ai?1,n?xi??x1??xi?ai?1,n?000?ai?2i?2n?1,n?xnx1x2x3?xn或从第n行开始，后一行减去前一行x1a12a13?a1n0x2?a12a23?a13?a2n?a1n按第一列展开nDn?00x3?a23?a3n?a2n?x1??xi?ai?1,n??????i?2000?xn?an?1,n3.从第一行开始，前一行减去后一行01?1111?1111?01-x?11按第一列展开1?x1?11r2??1?x?r0x?1D=????????1?n?101?x?11???1?n?101?x?00?1-x1????????1x?x100?1?x1n?100?11?1111?1101?1101?11???1?n?1x01?x?11???1?n?1x01?x?11??????????00?1?x100?1?x1n?111?11按第一列展开1?x1?11???1?n?1x01?x?11?????1?n?1xn?3111?????1?x1???1?n?xn?2200?1?x1n?2
11xx11??1?x1n?1
ax三、1.左边?ayaz2ayazaxazbybzbxbybxby?abz3?2a?3?3?2b?3?3?2c?3?3?2d?3?3xyzyzxzx?by3yzxzxyxy?右边 zax?bzay2bxac3-c2?a?1??b?1??c?1??d?1?2a?32b?32c?32d?32.左边=bcd22c4-c122?0?右边
22二、按1.最后一行展开D?an??1??x?a1x1加边n?1??1?n?1?an?1??1?n?2x??1?n?2???a2??1?2n?1xn?2??1???x?a1?xn?1
nn?1?a2x1n?2???an?1x?an??????1?ann?1111+a2?1111?1??1??11a10?010a2?0?????1?0?a1a2?an?1???an1aiCi，i?2,3,?n),变成三角形行列式才写出结果。00???????Dn?1???Dn?200?01+a11?10n2.Dn??i?11??ai?注意：这里简写了步骤，鸡爪型行列式要经过列变(C1+?按第一列展开0?????00??????003.因Dn??????Dn?1????1?1?2?00
????????所以Dn??Dn?1???Dn?1??Dn?2???2?Dn?2??Dn?3???n?2?D2??D1?
又D2?????????22???????，D1????????
代入上式得Dn??Dn?1??2 （1），同理可得Dn??Dn?1??2 （2）
??n?1由（1）、（2）解得Dn??n?1???
?1?4.C1????Ci,i?2,3,?,n?i?n5.先r1???rn,r2???rn?1,?,再c1???cn,c2???cn?1?100?010?1??n!????0i?i?2??nn?i?2?1?????i?00?0120?0103?0?????1a?nD??1a??n?1??n?1n?1?????1a?an?1D???a?n??a??n?1????i?j?1?j?i?n?1?a?n?n?a??n?1??nann?1