This course on Linear Algebra aims to teach students how to solve systems of linear equations, understand matrix operations, determine linear independence, work with determinants, explore vector spaces, and analyze eigenvectors and eigenvalues. The course covers various topics such as row reduction, matrix transformations, orthogonal projections, and least squares problems. The teaching method involves lectures, examples, and practical applications. This course is intended for individuals interested in gaining a solid foundation in linear algebra concepts and applications.
Overview
Syllabus
Linear Algebra 1.1.1 Systems of Linear Equations.
Linear Algebra 1.1.2 Solve Systems of Linear Equations in Augmented Matrices Using Row Operations.
Linear Algebra 1.2.1 Row Reduction and Echelon Forms.
Linear Algebra 1.2.2 Solution Sets and Free Variables.
Linear Algebra 1.3.1 Vector Equations.
Linear Algebra 1.3.2 Linear Combinations.
Linear Algebra 1.4.1 The Matrix Equation Ax=b.
Linear Algebra 1.4.2 Computation of Ax.
Linear Algebra 1.5.1 Homogeneous System Solutions.
Linear Algebra 1.5.2 Non-Homogeneous System Solutions.
Linear Algebra 1.6.1 Applications of Linear Systems - Economic Sectors.
Linear Algebra 1.6.2 Applications of Linear Systems - Network Flow.
Linear Algebra 1.7.1 Linear Independence.
Linear Algebra 1.7.2 Special Ways to Determine Linear Independence.
Linear Algebra 1.8.1 Matrix Transformations.
Linear Algebra 1.8.2 Introduction to Linear Transformations.
Linear Algebra 2.1.1 Matrix Operations - Sums and Scalar Multiples.
Linear Algebra 2.1.2 Matrix Operations - Multiplication and Transpose.
Linear Algebra 2.2.1 The Inverse of a Matrix.
Linear Algebra 2.2.2 Solving 2x2 Systems with the Inverse and Inverse Properties.
Linear Algebra 2.2.3 Elementary Matrices And An Algorithm for Finding A Inverse.
Linear Algebra 2.3.1 Characterizations of Invertible Matrices.
Linear Algebra 3.1.1 Introduction to Determinants.
Linear Algebra 3.1.2 Co-factor Expansion.
Linear Algebra 3.2.1 Properties of Determinants.
Linear Algebra 4.1.1 Vector Spaces.
Linear Algebra 4.1.2 Subspace of a Vector Space.
Linear Algebra 4.2.1 Null Spaces.
Linear Algebra 4.2.2 Column Spaces.
Linear Algebra 4.3.1 Linearly Independent Sets and Bases.
Linear Algebra 4.3.2 The Spanning Set Theorem.
Linear Algebra 4.5.1 The Dimension of a Vector Space.
Linear Algebra 4.5.2 Subspaces of a Finite Dimensional Space.
Linear Algebra 4.6.1 The Row Space.
Linear Algebra 4.6.2 Rank.
Linear Algebra 5.1.1 Eigenvectors and Eigenvalues.
Linear Algebra 5.1.2 More About Eigenvectors and Eigenvalues.
Linear Algebra 5.2.1 Determinants and the IMT.
Linear Algebra 5.2.2 The Characteristic Equation.
Linear Algebra 6.1.1 Inner Product, Vector Length and Distance.
Linear Algebra 6.1.2 Orthogonal Vectors.
Linear Algebra 6.2.1 Orthogonal Sets.
Linear Algebra 6.2.2 Orthogonal Projections.
Linear Algebra 6.3.1 Orthogonal Decomposition Theorem.
Linear Algebra 6.3.2 The Best Approximation Theorem.
Linear Algebra 6.5.1 Least Squares Problems.
Taught by
Kimberly Brehm
