Determinants of Matrices

The determinant of a matrix is a scalar value that can be calculated from the elements of the matrix. It is denoted by $\small \det(A)$ or $\small |A|$.

$$\det\begin{bmatrix}\ a & b\\ c & d\\ \end{bmatrix}=ad-cb$$

$$\det\begin{bmatrix} a & b & c\\ d & e & f\\ g & h & i \end{bmatrix}=a\begin{vmatrix} e & f\\ h & i \end{vmatrix}-b\begin{vmatrix} d & f\\ g & i \end{vmatrix}+c\begin{vmatrix} d & e\\ g & h \end{vmatrix}$$

The pattern continues for larger matrices, here is an example of a 4x4 matrix determinant by Byju’s.

Sources #

• Wikipedia
• Khan Academy