Determinants: Are mathematical objects that are very useful

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 equations has a unique solution iff the determinant of the system's matrix is nonzero (i.e., the matrix is nonsingular). This page provides an extensive overview of determinants in linear algebra, detailing their definitions, properties, and computation methods, particularly through row reduction. It emphasizes the … The determinant of a matrix is a scalar value that can be calculated for a square matrix (a matrix with the same number of rows and columns). It serves as a scaling factor that is used for the transformation of a matrix. NCERT