# MATH10120 Linear Algebra with Applications to Economics

This course offers a first introduction to linear algebra, and is tailored to meet the needs of students in Economics & Finance. During the course of this module students will be introduced to matrix algebra, the Gauss-Jordan algorithm, methods of computing eigenvalues and eigenvectors of a matrix, the theory of determinants, properties of real vector spaces. Applications of these topics to economics are described at regular intervals and given as motivation for their study. These include Leontief input/output models and Markov chains.

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Curricular information is subject to change

Learning Outcomes:

On completion of this module students should be able to:
-Perform a number of algorithms using techniques from linear algebra
-Model linear problems in economics in the context of linear algebra and matrices
-Solve such problems by applying algorithms learned in the course of this module
-Advance to an intermediate level course in linear algebra

Indicative Module Content:

• Systems of Linear Equations
o Definition of Matrix and first properties
o Elementary Row Operations
o Matrix in row echelon form and reduced echelon form
o Gauss-Jordan Algorithm

• Matrix Algebra
o Sum of matrices
o Product between a number and a matrix
o Product between two matrices
o Transpose and properties
o Inverse and properties
o Determinant and properties
o Rank of matrix
o Linear systems and inverse

• Vectors Spaces, Linear Transformations and Applications
o Definition of space and subspace
o Linearly independent vectors
o Basis of a vector space
o Linear Transformations and properties
o Linear Transformations and linear systems
o Row operations, linear transformations and determinants

• The Leontief Input-Output Model

• Eigenvalues and Eigenvectors
o Definition and properties
o Eigenvalues and Eigenvector computation
o Diagonalizable Matrices

• Markov chain

Student Effort Hours:
Student Effort Type Hours
Lectures

30

Tutorial

12

Specified Learning Activities

20

Autonomous Student Learning

38

Total

100

Approaches to Teaching and Learning:
Lectures, tutorials, enquiry and problem-based learning
Requirements, Exclusions and Recommendations
Learning Requirements:

At least H4 (or equivalent) in Higher Level Leaving Certificate Mathematics.

Module Requisites and Incompatibles
Incompatibles:
ECON10030 - Intro Quantitative Economics, MATH10030 - Maths for Business, MATH10050 - Linear Algebra & Geom, MATH10090 - Matrices & Vectors, MATH10200 - Matrix Algebra, MATH10250 - Intro Calculus for Engineers , MATH10270 - Linear Algebra in the Math Sci, MATH10280 - Linear Algebra in the Phys.Sci, MATH10290 - Linear Algebra for Science, MATH10340 - Linear Algebra 1 (MPS), MATH20130 - Fund. Actuarial Mathematics I, MST10030 - Linear Algebra I

Assessment Strategy
Description Timing Open Book Exam Component Scale Must Pass Component % of Final Grade

Not yet recorded.

Carry forward of passed components
No

Resit In Terminal Exam
Spring Yes - 2 Hour