Become a Linear Algebra Master
The course described provides an extensive exploration of Linear Algebra through a variety of teaching materials, including video lessons and text explanations. It is segmented into numerous sections that cover fundamental and advanced topics such as operations on matrices, matrix-vector products, transformations, and properties of vectors and spaces. Each topic includes practical applications such as solving linear systems, matrix multiplication, and exploring vector spaces and transformations. Additionally, the course offers quizzes for assessment and workbooks for extra practice to ensure thorough understanding and application of the concepts taught. Special topics include orthogonality, basis changes, and eigenvalues and eigenvectors. This structured approach aims to simplify complex Linear Algebra concepts for better learning and comprehension.
Skills for certificate:
Linear Algebra
Algebra
Mathematics
Problem Solving
Critical Thinking
Become a Linear Algebra Master
UC-753c138c-b4f5-47fa-bb8a-5eb0db6203de
Description
The course described provides an extensive exploration of Linear Algebra through a variety of teaching materials, including video lessons and text explanations. It is segmented into numerous sections that cover fundamental and advanced topics such as operations on matrices, matrix-vector products, transformations, and properties of vectors and spaces. Each topic includes practical applications such as solving linear systems, matrix multiplication, and exploring vector spaces and transformations. Additionally, the course offers quizzes for assessment and workbooks for extra practice to ensure thorough understanding and application of the concepts taught. Special topics include orthogonality, basis changes, and eigenvalues and eigenvectors. This structured approach aims to simplify complex Linear Algebra concepts for better learning and comprehension.
Learning Objectives
- Introducing and performing operations on one and two matrices, including addition, subtraction, scalar multiplication, and multiplication.
- Solving linear systems with two or three unknowns using matrices and row operations, and applying Gauss-Jordan elimination to determine the number of solutions.
- Defining matrix dimensions and entries, representing systems with matrices, identifying pivot entries, achieving row-echelon forms, and using elimination matrices for transformations.
- Understanding zero and identity matrices, matrix-vector products, manipulating vectors, and performing vector operations including dot and cross products.
- Creating linear combinations, defining span, determining linear independence, and exploring linear subspaces and bases for vector spaces.
- Exploring the null space and column space of a matrix, and solving Ax=0 and Ax=b for specific vectors.
- Introducing and analyzing linear transformations, utilizing transformation matrices, and exploring concepts of image, preimage, and kernel.
- Understanding and reversing transformations to find inverses, evaluating invertibility, and differentiating between invertible and singular matrices.
- Calculating and modifying determinants, applying Cramer's rule, and using determinants to find area, with a focus on upper and lower triangular matrices.
- Introducing matrix transposes, exploring their properties, and performing A=LU factorization.
- Finding orthogonal complements, projecting onto subspaces, finding least squares solutions, changing coordinates, and applying the Gram-Schmidt process for orthonormal bases.
- Introducing eigenvalues and eigenvectors, determining eigenspaces, and exploring these concepts in three dimensions.