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.

Matrix Inverse

Linear systems of equations

Linear systems in matrix notation


Inverse, determinants and linear systems: Problems

Exercises on matrix inverse, determinants and linear systems

Problem: Determinants

Problem: Determinants

Problem: Matrix inverse

Problem: Matrix inverse

Problem: Matrix inverse

Problem: Matrix inverse and matrix transpose

Problem: Matrix equation

Problem: Matrix algebra

Problem: Linear equations

Problem: System of four equations

Problem: System of equations in matrix form