Two Linear Equations in Two Unknowns
Kick things off with a pair of equations in a pair of unknowns.
Linear algebra is pervasive in just about all modern scientific subjects, including physics, mathematics, computer science, electrical engineering, economics, and aeronautical engineering. You’ll learn about its applications in computer graphics, signal processing, machine learning, RLC circuit analysis, and control theory.
By the end of this course, you’ll be able to solve systems of equations of all flavors and complexities using linear algebra, from a simple 2x2 matrix equation to much more complex systems involving many variables.
Multiple variables, multiple equations - no worries!
Kick things off with a pair of equations in a pair of unknowns.
Increase the challenge with three equations in three unknowns.
Learn a general algorithm for solving systems of equations.
Look deeper into the math behind Gauss-Jordan reduction.
Practice solving linear systems with electrical engineering problems.
Explore the power of vectors with magic squares, spanning sets, and more...
What is the essence of a vector?
Discover what it means to have a space within a space.
Learn how to spot redundant vectors.
What measures the size of a vector space?
What's the connection between vectors and geometry?
Apply your linear algebra knowledge to an important problem in statistics.
A fundamental building block for linear algebra.
Find out what matrices and vectors share in common.
Is it ever OK to divide by a matrix?
See what the column, row, null and transpose kernel spaces have to say about a matrix.
Practice fundamental matrix concepts on a graph theory application.
Determinants, maps, bases, and more.
Learn how to turn vectors into... other vectors.
Uncover the deep connection between linear transformations and matrices.
Discover a simple test for matrix invertibility.
Explore some beautiful and useful properties of determinants.
Formalize the relationship between matrices and linear transformations.
What makes two matrices similar?
Use determinants to fit a polynomial to a collection of data.
Eigenvalues, eigenvectors, and applications!
Learn to work with special vectors of fundamental importance.
Learn a surefire way to find eigenvalues.
When can a matrix be put into a diagonal form?
Sample some of the uses of diagonalization in graph theory and probability.