MATH-111(g): Linear Algebra

Lectures in this course (57)

Explores elementary matrices, inverses, uniqueness of solutions, and linear transformations in linear algebra.

Introduces LU decomposition for efficient linear equation solving using matrix factorization.

Covers the LU decomposition method for matrix factorization and its application in electrical engineering.

Covers the definition and properties of determinants, including the rule of Sarrus for 3x3 matrices.

Covers the calculation of determinants and determining matrix invertibility based on parameter values.

Explores Cramer's Rule for solving linear equations and calculating matrix inverses.

Covers Cramer's Rule for solving linear equations and calculating matrix inverses.

Covers the definition of vector spaces, subspaces, and linear combinations of vectors.

Explores solutions of linear equations, null spaces, subspaces, vector spaces, linear independence, bases, and dimensions.

Explores matrix determinants, linear independence, and bases in vector spaces.

Explores linear independence, bases, and dimension in vector spaces with examples involving matrices and polynomials.

Explores bases, dimensions, and matrix ranks in vector spaces with practical examples and proofs.

Explores matrix rank, subspaces, and their role in solving linear systems of equations.

Explores subspaces, matrix equations, linear transformations, and their matrix representations in linear algebra.

Covers kernels and images of linear transformations between vector spaces, illustrating properties and providing proofs.

Covers the concepts of kernel and image of a linear transformation and their relationship with the rank of the matrix.

Covers kernels and images of linear transformations between vector spaces.

Covers the determination of matrices associated with linear transformations and explores the kernel and image concepts.

Covers the method to calculate the images of vectors in a given base.

Covers the reduction of matrices, eigenvalues, eigenvectors, and geometric interpretations in vector spaces.

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