Menghitung Determinan Matriks Blok Menggunakan Ekspansi Laplace

Abstract

A matrix is ​​an arrangement of numbers, symbols or expressions arranged in rows and columns to form a square. The matrix was first conceived by Arthur Caley in 1859 in the study of systems of linear equations and linear transformations. In matrix theory, the calculation of determinants is one of the studies that is often discussed. Calculation of the determinant associated with a small matrix (n ≤ 3) is usually never a problem, only using the definition of the determinant can usually be solved immediately. However, calculating the determinant of a matrix with a large size is difficult to do if you only use the definition of the determinant. Several methods that can be used to calculate the determinant of a matrix are row reduction method, Laplace/cofactor expansion method and Schur's complement method. Another method that can be used is to change the matrix into a block matrix. To determine the determinant of the block matrix, the writer in this writing will use one of the methods, namely the Laplace/cofactor expansion method.