Quantitative Methods Lecture 4 Determinants and Systems of linear equations •BAKVM Outline of the lecture •Determinants • •Systems of linear equations • •Linear mappings The determinant of a square matrix The determinant of a square matrix The determinant of a square matrix The determinant of a square matrix Laplace expansion of the determinant Laplace expansion of the determinant Laplace expansion of the determinant Laplace expansion of the determinant Laplace expansion of the determinant Laplace expansion of the determinant Three theorems on the determinant The geometrical meaning of the determinant The transposed matrix Some properties of the determinant Some properties of the determinant To compute the determinant practically… To compute the inverse matrix practically… Systems of linear equations •System of linear equations • •Gaussian elimination • •Cramer’s rule A system of linear equations A system of linear equations Frobenius’ Theorem A system of linear equations A system of linear equations To solve a system of linear equations practically… To solve a system of linear equations practically… Cramer’s Rule Cramer’s Rule