线性代数 如图 n阶行列式 请举例说明!例如4阶行列式!
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线性代数 如图 n阶行列式 请举例说明!例如4阶行列式!
![](http://img.wesiedu.com/upload/6/95/695ba62b1c29c60492e17a72a03a8891.jpg)
![](http://img.wesiedu.com/upload/6/95/695ba62b1c29c60492e17a72a03a8891.jpg)
![线性代数 如图 n阶行列式 请举例说明!例如4阶行列式!](/uploads/image/z/16173542-38-2.jpg?t=%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B0+%E5%A6%82%E5%9B%BE+n%E9%98%B6%E8%A1%8C%E5%88%97%E5%BC%8F+%E8%AF%B7%E4%B8%BE%E4%BE%8B%E8%AF%B4%E6%98%8E%21%E4%BE%8B%E5%A6%824%E9%98%B6%E8%A1%8C%E5%88%97%E5%BC%8F%21)
其实这个不用搞懂,你反正也不会用定义去求n阶行列式的值.
四阶的计算如下,一共24项
A =
a11 a12 a13 a14
a21 a22 a23 a24
a31 a32 a33 a34
a41 a42 a43 a44
= a11a22a33a44 - a11a22a34a43 - a11a23a32a44 + a11a23a34a42
+ a11a24a32a43 - a11a24a33a42 - a12a21a33a44 + a12a21a34a43
+ a12a23a31a44 - a12a23a34a41 - a12a24a31a43 + a12a24a33a41
+ a13a21a32a44 - a13a21a34a42 - a13a22a31a44 + a13a22a34a41
+ a13a24a31a42 - a13a24a32a41 - a14a21a32a43 + a14a21a33a42
+ a14a22a31a43 - a14a22a33a41 - a14a23a31a42 + a14a23a32a41
四阶的计算如下,一共24项
A =
a11 a12 a13 a14
a21 a22 a23 a24
a31 a32 a33 a34
a41 a42 a43 a44
= a11a22a33a44 - a11a22a34a43 - a11a23a32a44 + a11a23a34a42
+ a11a24a32a43 - a11a24a33a42 - a12a21a33a44 + a12a21a34a43
+ a12a23a31a44 - a12a23a34a41 - a12a24a31a43 + a12a24a33a41
+ a13a21a32a44 - a13a21a34a42 - a13a22a31a44 + a13a22a34a41
+ a13a24a31a42 - a13a24a32a41 - a14a21a32a43 + a14a21a33a42
+ a14a22a31a43 - a14a22a33a41 - a14a23a31a42 + a14a23a32a41