24.1 - Definition of Vector Space
Enroll to start learning
You’ve not yet enrolled in this course. Please enroll for free to listen to audio lessons, classroom podcasts and take practice test.
Practice Questions
Test your understanding with targeted questions
What is a vector space?
💡 Hint: Think about sets with certain operations defined.
Name one axiom of vector spaces.
💡 Hint: This axiom ensures addition stays non-exit.
4 more questions available
Interactive Quizzes
Quick quizzes to reinforce your learning
What is the definition of a vector space?
💡 Hint: Recall the structure of vector spaces.
True or False: The zero vector is the additive identity in a vector space.
💡 Hint: Think about how adding zero affects numbers.
1 more question available
Challenge Problems
Push your limits with advanced challenges
Given a set of vectors in ℝ³ defined by V = {(x, y, z) | x + 2y + 3z = 0}, prove whether it is a subspace.
💡 Hint: Think about how the definition of V interacts with the properties of subspaces.
Explain how the properties of vector spaces can apply when creating a model of a bridge using forces as vectors.
💡 Hint: Consider how vectors represent directions and magnitudes.
Get performance evaluation
Reference links
Supplementary resources to enhance your learning experience.