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