CurrMap-1

Linear Algebra (H)

Time Frame

Semester

Content Presented

• Lines and Planes in 3-space
• Systems of equations
• Linear Independence
• Linear Transformations
• Properties of determinants
• Matrix Algebra
• Vector spaces, subspaces, null spaces, bases, rank and related theorems
• Systems of equations; eigenvector/eigenspace analysis
• Orthogonality and Least Squares Analysis
• Projects in economics and ecology

Skills Taught

• Finding vector equations/representations of lines and places in space
• Representing systems with matrices; solving systems with row operations and Cramer’s rule
• Determining necessary and sufficient conditions for linear independence and its implications
• Determining when transformations are linear, what the properties of linear transformations are.
• Using linear transformations to represent translocations in space;
• Properties and manipulations of determinants

• Basic operations of matrix algebra (matrix and scalar multiplication, inverses, transposes, anti-commutativity, partitions, and factorizations);
• Application of matrices to computer graphics;
• Spatial projections and transformations;

• Change of basis, determining independence of systems, dimensions of solution spaces, redundancy of solutions, spanning of subspaces
• Application to Markov chains, Leontief models
• Application to difference equations, discrete dynamical systems, systems in ecology and electrical circuits; differential equations
• Use of dot product, applications of least-squares analysis to linear models

Assessment of Student Knowledge

1. Quizzes, Problem Sets, and practicars (ungraded quizzes)
2. Individual conferences/tutorials
3. Monthly tests
4. Independent Study Projects
5. Semester Examination