In mathematics, the determinant is a scalar -valued function of the entries of a square matrix. The determinant of a matrix A is commonly denoted det (A), det A, or |A|. Its value characterizes some …

To work out the determinant of a 3×3 matrix: Multiply a by the determinant of the 2×2 matrix that is not in a 's row or column. As a formula (remember the vertical bars || mean "determinant of"): "The …

Dec 22, 2025 · Determinants are mathematical objects that are very useful in the analysis and solution of systems of linear equations. As shown by Cramer's rule, a nonhomogeneous system of linear …

In this section, we define the determinant, and we present one way to compute it. Then we discuss some of the many wonderful properties the determinant enjoys.

Dec 3, 2025 · Determinant, in linear and multilinear algebra, a value, denoted det A, associated with a square matrix A of n rows and n columns.

Learn some ways to eyeball a matrix with zero determinant, and how to compute determinants of upper- and lower-triangular matrices. Learn the basic properties of the determinant, and how to apply them. …

The determinant of a matrix has various applications in the field of mathematics including use with systems of linear equations, finding the inverse of a matrix, and calculus.