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 …

This page provides an extensive overview of determinants in linear algebra, detailing their definitions, properties, and computation methods, particularly through row reduction.

Nov 20, 2025 · To understand how determinants are evaluated, let us go through the process step by step, starting from the simplest 1×1 matrix and gradually moving to more complex and special cases.

Learn about what the determinant represents, how to calculate it, and a connection it has to the cross product. When we interpret matrices as movement, there is a sense in which some matrices stretch …

Determinants are the scalar quantities obtained by the sum of products of the elements of a square matrix and their cofactors according to a prescribed rule. They help to find the adjoint, inverse of a …

Dec 3, 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 …

Cofactor expansion, sometimes called the Laplace expansion, gives us a formula that can be used to find the determinant of a matrix A from the determinants of its submatrices.

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 is a number associated with any square matrix; we’ll write it as det A or |A|. The determinant encodes a lot of information about the matrix; the matrix is invertible exactly when the …