Linear Algebra

Dive into a comprehensive 11-hour course on Linear Algebra, covering fundamental concepts and advanced topics. Begin with systems of linear equations and matrix operations, progressing through vector spaces, determinants, and eigenvalues. Explore practical applications in economic sectors and network flow. Master techniques such as row reduction, linear transformations, and orthogonal projections. Develop a strong foundation in linear independence, inverse matrices, and least squares problems. Gain proficiency in solving complex mathematical challenges and understanding the theoretical underpinnings of Linear Algebra through a structured curriculum designed to build your skills progressively.

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.