解题方法
1 . 对于任意实数
,引入记号
表示算式
,即
,称记号
为二阶行列式.
是上述行列式的展开式,其计算的结果叫做行列式的值.
(1)求下列行列式的值:
①
;②
;
(2)求证:向量
与向量
共线的充要条件是
;
(3)讨论关于
的二元一次方程组
有唯一解的条件,并求出解.(结果用二阶行列式的记号表示).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d10449bc77d692a7270e0f20a68cdf2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa5440a1b5d9338efd6976a56432e100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43f9683760df4268272525c8082c7ee5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0c8894e0b37af5da23a1c1bffb32017.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa5440a1b5d9338efd6976a56432e100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43f9683760df4268272525c8082c7ee5.png)
(1)求下列行列式的值:
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c601a13b26ec4fe000e79cf189d9bdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4c5a0d1545e308e320a49e1c305ea90.png)
(2)求证:向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7ef9b43b03c19f5616e31888f053915.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2502935b71dab102edbe6f162046943.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9069422cc832b478cd86186e5f22897.png)
(3)讨论关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b0fffbec1fe851795dfdd448bf0d165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f334249bbad594a5db5137164b79f1d.png)
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解题方法
2 . 对于任意实数a,b,c,d,表达式
称为二阶行列式(determinant),记作
,
(1)求下列行列式的值:
①
;②
;③
;
(2)求证:向量
与向量
共线的充要条件是
;
(3)讨论关于x,y的二元一次方程组
(
)有唯一解的条件,并求出解.(结果用二阶行列式的记号表示).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43f9683760df4268272525c8082c7ee5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2969b2ffdf4b488198859e5d2ee5686.png)
(1)求下列行列式的值:
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071bf9c126b47ea5224c18f75d9942e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad13c820abe381c7f10dcae33e1b0bbf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e92b3f185ae61e892456c4d7d5bc880.png)
(2)求证:向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b8b86cea449d67ea9b0b5f875fc83c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3b584818e24e4c000fdff3916e8b7c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b1eb002f0e496dcf81cbc0e9c5c8460.png)
(3)讨论关于x,y的二元一次方程组
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38c1ef63c57a969fa3ffe9bbe3b06adb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1cfd5c7c9f8891c3e3a8f89566fa09f5.png)
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3 . 已知方程组![](https://staticzujuan.xkw.com/quesimg/Upload/formula/267ad467cfcbcc2dff5b77665f13a8e2.png)
(1)求证:方程组恰有一解;
(2)求证:以方程的解
为坐标的点在一条直线上;
(3)求
的最小值,并求此时a的范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/267ad467cfcbcc2dff5b77665f13a8e2.png)
(1)求证:方程组恰有一解;
(2)求证:以方程的解
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82a79a33a83a7ba57a34b5093d1d1d02.png)
(3)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dbd4d32dcc1445563887de5d3ab7fb7.png)
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