Introductory Linear Algebra

The first of the two courses will introduce systems of equations, which live at the heart of linear algebra. In this course you will explore fundamental concepts by exploring definitions and theorems that give a basis for this subject. You will apply an algorithm for solving linear systems that will be used for computations and for gaining insight into the properties of linear systems. This insight will all you to reduce problems involving linear combinations of vectors to approaches that involve systems of linear equations. You will also explore linear independence and linear transformations. They have an essential role throughout applications of linear algebra in many areas of industry, science, and engineering.

In the second of these two courses you will see how we can apply the Invertible Matrix Theorem to describe how a square matrix might be used to solve linear equations. This theorem is a fundamental role in linear algebra, as it synthesizes many of the concepts introduced in the first course into one succinct concept. You will then explore theorems and algorithms that will allow you to apply linear algebra in ways that involve two or more matrices. You will examine partitioned matrices and matrix factorizations, which appear in most modern uses of linear algebra. You will also explore two applications of matrix algebra, to economics and to computer graphics.

What you'll learn

• Evaluate mathematical expressions to compute quantities that deal with linear systems.
• Construct an LU factorization of a matrix and use it to solve linear systems of equations.
• Apply matrix algebra and linear transformations to solve and analyze problems in computer graphics and economics.
• Apply subspaces and invertibility to characterize and analyze matrices and solution sets of linear systems.