1 . 设数阵
,其中
.设![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac98f22d559df85afd6cde2122982c1b.png)
,其中
,
且
.定义变换
为“对于数阵的每一列,若其中有t或
,则将这一列中所有数均保持不变;若其中没有t且没有
,则这一列中每个数都乘以
”(
),
表示“将
经过
变换得到
,再将
经过
变换得到
,…,以此类推,最后将
经过
变换得到
.记数阵
中四个数的和为
.
(1)若
,
,写出
经过
变换后得到的数阵
,并求
的值;
(2)若
,
,求
的所有可能取值的和;
(3)对任意确定的一个数阵
,证明:
的所有可能取值的和不大于
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd0a32496c35c7a9ec330bdd02808829.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d989c2c5a405c4d9a20e470f5bd96ab3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac98f22d559df85afd6cde2122982c1b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44f8daacbdbb8b2ff092d4c56057c729.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a96b51fbf91d105af6afbd5b2966185a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b08c58baacec3cd0c0a06e267fa9ec5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c88248a34d270530f9d01570a911878.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4e93d044f7bde4330e206b4edd2bd06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97add95cc99b7846691dbdd91ef0f3bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97add95cc99b7846691dbdd91ef0f3bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acbc6a613224461ade69362d46550474.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34b2c2aa49dc4520fcc7fe01f1776301.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ad42dbc5fa989573d079ff58c9bd837.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd680d9d3352bfe69d373054ab106a0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc9e38f3101bb9a37b307ce245c57b73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/096b1ece1dcd29c59a46a4b3e02cb548.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/096b1ece1dcd29c59a46a4b3e02cb548.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/841f2788fc89aafb399653dcf5c373c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5031a3a951c4a1d1c5e9f80a5e26513.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3233aed5e30e9988e1676b4392dd4dab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a6254dbc0b14828d000e1901ae21eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9cce113f874ea096ee027d0c7d2ad27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9cce113f874ea096ee027d0c7d2ad27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ca99f73e0e80bfa74b06d4d28ed09c4.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d21f1d68a3e838d14d000d02301ce78c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e39979f11a0fd0a8d9d726a1b48260f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd680d9d3352bfe69d373054ab106a0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7df1d9b712b639c8b6809c9f3ae03706.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/096b1ece1dcd29c59a46a4b3e02cb548.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ca99f73e0e80bfa74b06d4d28ed09c4.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d21f1d68a3e838d14d000d02301ce78c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07225d468ccf6abe4f258d74cd8ba08f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ca99f73e0e80bfa74b06d4d28ed09c4.png)
(3)对任意确定的一个数阵
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd680d9d3352bfe69d373054ab106a0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ca99f73e0e80bfa74b06d4d28ed09c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6b9a5f1362c12e1ea8f6fc0d9d787ac.png)
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