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 …

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"): …

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 …

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

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 …

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, …

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 …

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.

Dec 3, 2025 · Determinants are of use in ascertaining whether a system of n equations in n unknowns has a solution. If B is an n × 1 vector and the determinant of A is nonzero, the …

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 …