1 . 由
个数排列成
行
列的数表称为
行
列的矩阵,简称
矩阵,也称为
阶方阵,记作:
其中
表示矩阵
中第
行第
列的数.已知三个
阶方阵分别为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9ff7824ff4c2d54281baa128c63235d.png)
,
,其中
分别表示
中第
行第
列的数.若
,则称
是
生成的线性矩阵.
(1)已知
,若
是
生成的线性矩阵,且
,求
;
(2)已知
,矩阵
,矩阵
是
生成的线性矩阵,且
.
(i)求
;
(ii)已知数列
满足
,数列
满足
,数列
的前
项和记为
,是否存在正整数
,使
成立?若存在,求出所有的正整数对
;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/767f5a4746f04db68386fac3970b1ed1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/767f5a4746f04db68386fac3970b1ed1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3f2dee59acd8ba55c25c9f5316ed3c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04b540e0e8df1cc4f59180460e7d4264.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7600d2cfbdc6146db96cc545706004f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9ff7824ff4c2d54281baa128c63235d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d39d394642b16525e70ecda2fd70cdb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0419a2c0acbb1af2d84373cca6d605a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d37e026f409868f81064617a4120e73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61cbe82b97961a419f24e40bf54a1376.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7600d2cfbdc6146db96cc545706004f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ddff15b8d9a8b8f371670b3cba489b4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d03e28332446eea06a9bd61050d38373.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c62349070fb07aaeffbb5d7d91289a9.png)
(1)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab241dfd5146035044bc35dcfb3e0994.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/647c97da671781944dcbac93af7cadcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64bb2b9e1f49aee4f4b91f0ba229fd75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28b7d9aa89f698d7ac2772dbf24a5a1e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/647c97da671781944dcbac93af7cadcb.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4246c1e8163f564afaf51cec2352362e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18ce6091ca3c6c454219a36f5396ccfa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d03e28332446eea06a9bd61050d38373.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c62349070fb07aaeffbb5d7d91289a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18d7859dc8659a974ea86d14b6ef18e6.png)
(i)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c07cbe067882d2f964195527ad1b33c.png)
(ii)已知数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44a8100f98999e472945ab7050af50d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b783cf91e34e692ce8e171f0965cb53f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa7ffcaea39899aa3e4a17f9a5bc46f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b783cf91e34e692ce8e171f0965cb53f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/280860dd039e1305a5ccc455f63e8223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdd0bd4520a95ff89c01f5db5d0a0b0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a64d924836b4292239d9726c6473d7f5.png)
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