解题方法
1 . 已知
是实常数,
.
(1)当
时,求函数
的单调增区间;
(2)是否存在
,使得
是与
有关的常数函数,求出所有满足条件的
,若不存在,说明理由
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc849f246ca0d82bac78beaf64b91c71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9c5dcfff2f777dbac390c16d7cb4de4.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/354ac956269627cbd3c4088fe344014d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(2)是否存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
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2 . 用行列式讨论下列直线的位置关系![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d71187e41a7278c6f1893852944bb782.png)
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56d4b99f920ce922c4709077a6662446.png)
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d71187e41a7278c6f1893852944bb782.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10d692c427b43ef979b55112687ccdf9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56d4b99f920ce922c4709077a6662446.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8b3be7c997a35b3277e1d3e0c9b0938.png)
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3 . 设2阶方矩阵
,则矩阵A所对应的矩阵变换为:
,其中
,
,其意义是把点
变换为点
,矩阵M叫做变换矩阵.
(1)当变换矩阵
时,点
,
经矩阵变换后得到点分别是
,
,求经过
,
的直线的方程;
(2)当变换矩阵
,点
经矩阵
的作用变换后得到点
,求实数m,n的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66226d08dd84a2e6dc096c3fcfc7e41c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc163fa0a2929ff019012aa3623088b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/909e45af90756a0dc1fee910b1661974.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8061249592e9502a68f0d5b52172724.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aee82283f06cedef32eb15b87964f5d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b08f646952c521d4f022af322b179a0a.png)
(1)当变换矩阵
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd8b0cf31caa3e7c5c7dced1559726f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a98ef6b26186130f8d88c66d3b3c78fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f87cae2228b72a1ec635860203496967.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5326817f9af012432a202749d1df59f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39e210795a966bd5dc1293479ab1988b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5326817f9af012432a202749d1df59f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39e210795a966bd5dc1293479ab1988b.png)
(2)当变换矩阵
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5184ca29a211cfb1c6b492993a608edd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/518dfce0a9aab04171383586c5077146.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f8fd27ebdd03bd80b1843c3f79e55ee.png)
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真题
4 . 在平面直角坐标系
中,设椭圆
在矩阵
对应的变换下得到曲线F,求F的方程,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a2db3534aaf21bbc27448be9ee90a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7fa12d00ceeffdd2025ea6ce19e351c.png)
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5 . 解不等式(x为未知数):
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdd6eafb3d6a522cd9cd419768d51687.png)
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6 . 用行列式讨论方程组
(
)解的情况.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78149a12d8892bc2a1f6d58568b4fcfb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22dd8b3dc4c609bab82d356a5cc2208d.png)
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7 . 设二阶矩阵
.
(1)求
;
(2)若曲线C在矩阵A对应的变换作用下得到曲线C:6x2-y2=1,求曲线C的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e12ce72dea3e08e90df1bdebfb1fbd5e.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a84646168f0afc4380043a52b818c35.png)
(2)若曲线C在矩阵A对应的变换作用下得到曲线C:6x2-y2=1,求曲线C的方程.
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8 . 已知
,直线
的方程为
,直线
的方程为
,利用行列式,讨论直线
和
的位置关系.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2725a89d93c791f7a0098f4964587905.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a0902f227ff600ed83f76274817bdd4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d573582c36f51ff73265dc18bc9349d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
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9 . 用行列式解关于
的方程组
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b0fffbec1fe851795dfdd448bf0d165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6b2c3f179071927c96631fe75d1e782.png)
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10 . 用行列式的方法解关于x,y的二元一次方程组
,并对解的情况进行讨论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c6f51653c53ff6d370dd964ebfc5065.png)
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