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设矩阵<img src='https://fb.fenbike.cn/api/planet/accessories/formulas?fontSize=18&latex=MSKhFnaVHp1U7eaSG76eGW55NWIuoVH_7A59mzaseEqYTH2UUUedLlP2d2rtOM8JiNaMzA4d2NdT-isiHpU9TS3ztNU_N1pdqQGo4_TiY9fJlbV_PMZfe-ToSyqBcYhJ1Dp-RCrIwXhruJtyVUv8dpyG8p1utyv58V7JvdYlT_Yft9YXLaYIESH6DTzJzRln' />,<img src='https://fb.fenbike.cn/api/planet/accessories/formulas?fontSize=18&latex=5r--XJAcuvJz2i0YNLewGrEyr75JrFUgaSYRLegRLtaBTSX7vIETZ0Ckceodi11LIfSh5hug7yhyE4ww4myW7HVHnrHiXEu3pJaW4a7w3a10vMphtCD1y0n3MSumotJXq3GcGtngqZ8MJv-Hmjh-E5L0S6E4qYYwiBpi3mGXwFJm_j9kOuRnRwKUjW16aLvP' />,<img src='https://fb.fenbike.cn/api/planet/accessories/formulas?fontSize=18&latex=3LHD15wpOVfxssOaY1trTgJoFnvHk4lDCbtlmAJxG7FurCgOkRqb2ldR-RsqVMgbhBusGU2jIapgHB_fmh6NFeczUYN90IqpDQKRbRMYvvGVTUtw7GsqFIklv8ClBduSMY1RTRzEvWs-j0B6hrBYxU-ywdPHgLRsTpC5MD0XoWeipXrMny9ALdzo6ene6ph5' />,若矩阵$<img src='https://fb.fenbike.cn/api/planet/accessories/formulas?fontSize=18&latex=fFNKsfANwBtd06ZJ24Gr37NO8UxWfVG7gjy0vJd5x-xOHNigFz1zfsgMEGof0TqAP4vMyBEujaBqYW6DOcu79Q' />,证明:<img src='https://fb.fenbike.cn/api/planet/accessories/formulas?fontSize=18&latex=lptJ65LLRkO8d745vxlCDWzrzupvlcYlWrxIkauzczg' />.

设矩阵,,,若矩阵$,证明:.

发布时间:2025-03-31 00:57:13
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答案:证明 对行列式做运算,将化为上三角行列式得.对行列式做运算,将化为上三角行列式得.对行列式的前行做与行列式相同的运算,对行列式的后行做与行列式:,因此,.可以类似地证明,.
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