Foundations: Subspaces and Determinants

This course is part of Foundations of Linear Algebra Specialization

Instructor: Macmillan Learning

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2 modules

Gain insight into a topic and learn the fundamentals.

Intermediate level

Some related experience required

1 week to complete

at 10 hours a week

Flexible schedule

Learn at your own pace

2 modules

Gain insight into a topic and learn the fundamentals.

Intermediate level

Some related experience required

1 week to complete

at 10 hours a week

Flexible schedule

Learn at your own pace

What you'll learn

Identify subspaces, determine bases and dimensions, perform changes of basis, and calculate determinants.

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This course is part of the Foundations of Linear Algebra Specialization

When you enroll in this course, you'll also be enrolled in this Specialization.

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There are 2 modules in this course

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.

In this module, you will examine subspaces and the concepts used to describe their structure. You will work with bases and dimensions, row and column spaces, and changes of basis. By applying these concepts in section-based problems, you will build your ability to characterize and work with subspaces.

What's included

4 readings7 assignments

4 readingsTotal 280 minutes

Introduction to Subspaces Reading50 minutes
Basis and Dimension Reading90 minutes
Row and Column Spaces Reading70 minutes
Change of Basis Reading70 minutes

7 assignmentsTotal 100 minutes

Introduction to Subspaces Graded Assignment10 minutes
Basis and Dimension Graded Assignment10 minutes
Row and Column Spaces Graded Assignment10 minutes
Change of Basis Graded Assignment10 minutes
Introduction to Subspaces Practice Assignment20 minutes
Basis and Dimension Practice Assignment20 minutes
Row and Column Spaces Practice Assignment20 minutes

In this module, you will study the determinant function and the properties of determinants. You will also examine applications of determinants and practice working with determinant-based problems. By the end of the module, you will be able to calculate determinants, use their properties, and apply determinant concepts in the contexts presented in the course.

What's included

3 readings6 assignments

3 readingsTotal 190 minutes

The Determinant Function Reading80 minutes
Properties of the Determinant Reading60 minutes
Applications of the Determinant Reading50 minutes

6 assignmentsTotal 94 minutes

The Determinant Function Graded Assignment10 minutes
Properties of the Determinant Graded Assignment10 minutes
Applications of the Determinant Graded Assignment18 minutes
The Determinant Function Practice Assignment20 minutes
Properties of the Determinant Practice Assignment20 minutes
Applications of the Determinant Practice Assignment16 minutes

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Instructor

Macmillan Learning

13 Courses303 learners

Offered by

Macmillan Learning

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