8.2. Determinants

The determinant of a matrix is a tool used in many applications of engineering, sciences, and mathematics.
Definition of determinant
A determinant of a matrix is a scalar number that replaces the bracket with vertical lines.
The determinant of A is denoted by det A. A determinate differs from a matrix in that it has actual value.
A determinant of order n is a determinant with n rows and n columns.
The value of a second-order (2 × 2) determinant is calculated in form

det[a11a12a21a22]=|a11a12a21a22|=a11a22−a12a21

image

 
By using the sign rule, each term is determined by the first row in the diagram |+−+−+−+−+|.
The value of a third-order (3

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