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 …

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 …

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

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"): …

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 …

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, …

6 days ago · 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 …

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 …

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.

Determinants are derived from matrices, and matrices come from systems of linear equations. So determinants are a part of mathematics called "linear algebra" or " matrix algebra".