1 . 已知矩阵
,
,
,计算:
(1)
;
(2)
;
(3)
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/310cb16b06b551cb79b801193650eeef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9f3e086c56b08a30b1165c1091d9ab3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8218236dd2b58f16d299e1e339cd19fe.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7fd2e0881dea2b5d4938ac48b2b1782d.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
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2 . 已知
.求证:
三点共线的充要条件是
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c39d023fc87895b0f26477e890074e3a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7358ff8d99126de46113bb1c1c50f726.png)
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3 . 函数
的最大值是_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd7e0eb84d9d19131a5978733e85276d.png)
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4 . 将
表示成一个三阶行列式为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2381668f5db54a7fa892766e9de93b48.png)
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5 . 若
,
,
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/380bbacf854e30e2e747fc286d2b9997.png)
______ ,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ccd4162c7d09f970cb77cadacdbe521.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8bb135a3dce94ad7e096125c558f7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acff9e018c7c4fe86a925669aef8c3cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4deef4b0c87148779c115f2bc889e76e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5b9628add5c8c3798d91b0da6e74f12.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/380bbacf854e30e2e747fc286d2b9997.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ccd4162c7d09f970cb77cadacdbe521.png)
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6 . 设
,计算:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05dcd0b803c5b77cd73add9eb136ad5c.png)
________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af26da329d5a2f07875856b3529952e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05dcd0b803c5b77cd73add9eb136ad5c.png)
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7 . 求关于
的方程组
,有唯一解的条件,并求在此条件下该方程组的解.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a14c388e1e2e5a2ff1ccf6caffbee0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2444f2183746892574776148af2d427b.png)
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8 . 利用行列式解下列方程组:
(1)
(2)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffb3514b340beb8f80f777434fe44dc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df433e7619c87cc589af5466630fd360.png)
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9 . 甲、乙、丙三人一起做一批零件,甲、乙两人合作,甲做8天乙做5天能够完成;甲、丙两人合作,甲做6天丙做9天能够完成;乙、丙两人合作,乙做10天丙做6天能够完成,那么甲、乙、丙单独做,各需多少天能够完成?
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10 . 已知
,
而且
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26e36047abddb41d610eee6b85c828f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45c63449124223980083da5af1386c02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46a70d32c64918aa4d1d9d3ce0bdbf7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d10449bc77d692a7270e0f20a68cdf2.png)
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