Linear Algebra (H)

Content and Skills

Content Presented	Skills Taught
Lines and Planes in 3-space	Finding vector equations/representations of lines and places in space
Systems of equations	Representing systems with matrices; solving systems with row operations and Cramer’s rule
Linear Independence	Determining necessary and sufficient conditions for linear independence and its implications
Linear Transformations	Determining when transformations are linear, what the properties of linear transformations are. Using linear transformations to represent translocations in space;
Properties of determinants	Properties and manipulations of determinant
Matrix Algebra	Basic operations of matrix algebra (matrix and scalar multiplication, inverses, transposes, anti-commutativity, partitions, and factorizations); application to computer graphics; spatial projections and transformations;
Vector spaces, subspaces, null spaces, bases, rank and related theorems	change of basis, determining independence of systems, dimensions of solution spaces, redundancy of solutions, spanning of subspaces Application to Markov chains, Leontief models
Systems of equations; eigenvector/eigenspace analysis	Application to difference equations, discrete dynamical systems, systems in ecology and electrical circuits; differential equations
Orthogonality and Least Squares Analysis	Use of dot product, applications of least-squares analysis to linear models
Independent study projects in economics and ecology

--Draulston 14:48, 14 August 2008 (CDT)