Talk:Mathematical Methods of Physics/Matrices

Being used as a sandbox
For $$n\geq 3$$, we define $$\left| \begin{pmatrix} a_{11} & a_{12} & \ldots & a_{1n} \\ a_{21} & a_{22} & \ldots & a_{2n} \\ \vdots & \vdots & \ddots & \vdots \\ a_{n1} & a_{n2} & \ldots & a_{nn} \\ \end{pmatrix}\right|=a_{11}\left| \begin{pmatrix} a_{22} & \ldots & a_{2n} \\ \vdots & \ddots & \vdots \\ a_{n2} & \ldots & a_{nn} \\ \end{pmatrix}\right|-a_{12}\left| \begin{pmatrix} a_{22} & \ldots & a_{2n} \\ \vdots & \ddots & \vdots \\ a_{n2} & \ldots & a_{nn} \\ \end{pmatrix}\right|$$