Matrix Singularity

A matrix is singular if its determinant is zero.
A 2x2 matrix \(\begin{bmatrix}a & b\\c & d\end{bmatrix}\) is singular if its determinat \(\begin{vmatrix} a & b\\c& d\end{vmatrix} = ad-bc = 0\).
A 3x3 matrix \(\begin{bmatrix}a_1 & b_1 & c_1\\a_2 & b_2 & c_2\\a_3 & b_3 & c_3\end{bmatrix}\) is singular if its determinant is equal to zero.

$$\begin{vmatrix}a_{11} & a_{12} & a_{13}\\a_{21} & a_{22} & a_{23}\\a_{31} & a_{32} & a_{33}\end{vmatrix} = a_{11}\cdot \begin{vmatrix} a_{22} & a_{23} \\ a_{32} & a_{33}\end{vmatrix} -a_{12}\cdot\begin{vmatrix} a_{21} & a_{23}\\a_{31} & a_{33}\end{vmatrix} + a_{13}\cdot\begin{vmatrix}a_{21} & a_{22}\\a_{31} & a_{32}\end{vmatrix} = $$ $$= a_{11}(a_{22}a_{33}-a_{23}a_{32}) - a_{12}(a_{21}a_{33}-a_{23}a_{31}) + a_{13}(a_{21}a_{32}-a_{22}a_{31}) = 0$$

Check singularity for 2x2 matrix.

\(a_{11}\) = \(a_{12}\) =
\(a_{21}\) = \(a_{22}\) =
\(\begin{vmatrix}a_{11}& a_{12} \\ a_{12}& a_{22}\end{vmatrix}\) =

Check singularity for 3x3 matrix.

\(a_{11}\) = \(a_{12}\) = \(a_{13}\) =
\(a_{21}\) = \(a_{22}\) = \(a_{23}\) =
\(a_{31}\) = \(a_{32}\) = \(a_{33}\) =
\(\begin{vmatrix}a_{11} & a_{12} & a_{13}\\a_{21} & a_{22} & a_{23}\\a_{31} & a_{32} & a_{33}\end{vmatrix}\) =