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【正文】 ? ?AA.AA 11 ?? ?因此有為整數(shù)時當(dāng) ,0 ???A,???? ?? AAA ? ? .???? A?例 1 求方陣 的逆矩陣 . ???????????343122321A解 343122321?A?,0? .1存在?? A,234 1211 ??A ,333 1212 ????A三、逆矩陣的求法 同理可得 ,2,6,6,2 23222113 ????? AAAA,2,5,4 333231 ????? AAA,222563462????????????????A得故 ?? ? AAA11???????????????22256346221 .11125323231???????????????,331212321???????????A .1151531132??????????????B解 331212321?A010430321???.,?,矩陣求出其逆若可逆是否可逆下列矩陣 BA例 2 010430321???0143 ???4? ,0? .A 可逆所以,333 2111 ???A? ,431 2212 ????A,531 1213 ??A.A,A,A,A,A,A341103333231232221????????同理可求得???????????????3323133222123121111 1AAAAAAAAAAAAA.???????????????315404133411151531132????B由于,0? .B 不可逆故,130231,3512,343122321????????????????????????????? CBA例 3 設(shè) .CAXBX ?使?jié)M足求矩陣解 ,02343122321???A?,0135 12 ???B., 11 都存在??? BA,111253232311????????????????A且,25 131 ??????????BCAXB ?又由 1111 ???? ?? CBAA X B BA.11 ???? CBAX于是 11 ??? CBAX????????????????
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