NEKG33 Mathematical methods for economists

Chapter 22 : Day 22: Matrices

By Lund University

Welcome to the matrix!

Introduction to matrices

In the first section of this chapter we introduce matrices. We will then look at some special matrices such as diagonal matrices and the identity matrix. We then look at the row and column vectors and vectors in general.

Matrices, definitions

Special matrices

Row- and column vectors

Vectors

Addition, scalar multiplication and transpose

We look at how to add to matrices and when you are allowed to add to matrices (same dimension). It is also possible to multiply and matrix by a scalar and we look at all the algebraic rules for matrix addition and scalar multiplication. In the final lecture we study the transpose of a matrix and related concepts such as symmetric matrices.

Matrix addition and scalar multiplication

Algebraic rules for matrix addition and scalar multiplication

Matrix transpose

Matrices: Problems

Exercises on matrices

Problem: Construct matrix

Problem: Add matrices

Problem: Matrix equality

Problem: Add and subtract matrices

Problem: Linear combinations of 2 column vectors

Problem: Linear combinations of 3 row vectors

Problem: Linear combinations of 2 column vectors backwards

Problem: What can you say about the components of a vector?

Problem: Linear combination of 2 vectors, find the constants

Problem: Matrix transpose

Problem: Symmetric matrices