行列式（三维）
计算3×3矩阵的行列式及其倒数的值。
| \(\normalsize detA=det{A}={\left|\begin{array}\\ a_{\small 11}& a_{\small 12}& a_{\small 13}\\ a_{\small 21}& a_{\small 22}& a_{\small 23}\\a_{\small 31}& a_{\small 32}& a_{\small 33}\\\end{array}\right|}\\ \) |
| det A -5 | |
| 1/ det A -0.2 |
| \(\normalsize \\ (1)\ detA={\large\displaystyle \sum_{\small j=1}^{\small n}}a_{\small ij}A_{\small ij},\hspace{20px}A_{\small ij}:\ cofactor\\ (2)\ {\left|\begin{array}\\ a_{\small 11}& a_{\small 12}& a_{\small 13}\\ a_{\small 21}& a_{\small 22}& a_{\small 23}\\a_{\small 31}& a_{\small 32}& a_{\small 33}\\\end{array}\right|}\\\hspace{25px}=a_{\small 11}{\left|\begin{array}\\ a_{\small 22}& a_{\small 23}\\ a_{\small 32}& a_{\small 33}\\\end{array}\right|}-a_{\small 12}{\left|\begin{array}\\ a_{\small 21}& a_{\small 23}\\ a_{\small 31}& a_{\small 33}\\\end{array}\right|}+a_{\small 13}{\left|\begin{array}\\ a_{\small 21}& a_{\small 22}\\ a_{\small 31}& a_{\small 32}\\\end{array}\right|}\\ (3)\ {\left|\begin{array}\\ a_{\small 11}& a_{\small 12}\\ a_{\small 21}& a_{\small 22}\\\end{array}\right|}=a_{\small 11}a_{\small 22}-a_{\small 21}a_{\small 12}\\ \) |
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