What is a Determinant?
A determinant is a special number that can be calculated from a square matrix. Determinants are very useful in algebra, particularly in solving systems of linear equations, and they have important properties and applications.
Properties of Determinants
- The determinant of a 2x2 matrix A, where A = [[a, b], [c, d]], is calculated as det(A) = ad - bc.
- Switching two rows of a matrix will change the sign of its determinant.
- If a matrix has two identical rows, its determinant is zero.
- The determinant of a triangular matrix is the product of its diagonal elements.
Calculate a Determinant
Want to test your understanding? Try calculating the determinant of these matrices: