Foundations: Subspaces and Determinants

Learn how to describe the structure of subspaces and use determinants in linear algebra problems. Drawing on content from Jeffrey Holt, author of Linear Algebra with Applications, published by Macmillan Learning, this course develops your understanding of the relationships within vector spaces and matrices. You will begin with subspaces, learning to identify their defining characteristics and determine their bases and dimensions. You will examine row and column spaces and practice changes of basis to represent vectors using different coordinate systems. You will then study the determinant function, learn how to calculate determinants, and apply their properties to matrices. Through examples and practice problems, you will connect these concepts to the applications presented in the course. Readings and homework give you opportunities to practice identifying subspaces, working with bases, and calculating determinants. The course includes approximately 11 hours of learning material. This course is part of the Foundations of Linear Algebra Specialization and can also be taken independently.