Lectures in course MATH-111(g): Linear Algebra

Provides details about Linear Algebra course logistics, exercise sessions, and exam information.

Covers linear equations, systems of linear equations, and matrices, including Gaussian elimination.

Covers the Gaussian elimination method for solving linear equations using row operations and equivalent matrices.

Explores solving linear equations, matrix uniqueness, and reduction methods with examples.

Explains the Gauss-Jordan elimination method for solving linear equations and discusses main and free variables.

Covers linear systems without free variables, unique solutions, and the existence theorem.

Explores solving systems of equations with parameters using matrices and Gaussian elimination.

Covers echelon matrices, vector equations, linear combinations, and vector spans in R^n.

Explores how vectors represent lines and planes in space using their components and equations.

Explores matrix equations, solutions, properties, and vector spaces in linear algebra.

Explores matrix equations, homogeneous systems, solutions, consistency, and properties.

Explores the concept of linear independence in vector spaces through definitions and illustrative examples.

Covers linear applications, properties, examples, and implications regarding the linearity of transformations.

Explains the matrix of linear applications and canonical matrices for transformations.

Explores linear transformations, matrices, and their properties, including surjectivity, injectivity, and symmetry operations.

Explores linear applications, matrices, injectivity, unique solutions, and matrix operations.

Covers the basic operations on matrices, including addition, scalar multiplication, and matrix multiplication.

Covers matrix operations, including multiplication, transposition, powers, and inverses, and explains how to determine if a matrix is invertible.

Covers matrix invertibility, determining if a matrix is invertible, calculating its inverse, and elementary matrices.

Covers elementary matrices, their types, properties, and invertibility.