NEKG33 Mathematical methods for economists
Chapter 24 : Day 24: Matrix inverse and determinants
By Lund University
Mathematicians love to invert things and matrices are no exception. Determinants will help us figure out when we can invert a matrix.
Matrix inverse, determinants and linear systems
We begin this section by looking at the inverse of a matrix and how to calculate the inverse of a 2 by 2 matrix. We then return to linear systems of equations and see that such systems can be written in matrix notation with a coefficent matrix. We also learn how the solution to a linear system, if it exists and is unique, is related to the inverse of the coefficient matrix. The final topic is determinants. For every square matrix we can calculate its determinant. The determinant is zero if and only if the matrix lacks an inverse.
Linear systems of equations
Linear systems in matrix notation
Inverse, determinants and linear systems: Problems
Exercises on matrix inverse, determinants and linear systems