Professional Courses
Industry-relevant training in Business, Technology, and Design to help professionals and graduates upskill for real-world careers.
Categories
Interactive Games
Fun, engaging games to boost memory, math fluency, typing speed, and English skills—perfect for learners of all ages.
Typing
Memory
Math
English Adventures
Knowledge
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 related to the topic.
Question 1
Easy
What are the three conditions for a subset to be a subspace?
💡 Hint: Think about both operations: addition and scalar multiplication.
Question 2
Easy
Give an example of a zero vector in R².
💡 Hint: What are the components that make a vector zero?
Practice 4 more questions and get performance evaluation
Interactive Quizzes
Engage in quick quizzes to reinforce what you've learned and check your comprehension.
Question 1
What is a key requirement for a subset to be a subspace?
- It must contain more than one vector
- It must contain the zero vector
- It must be infinite-dimensional
💡 Hint: Think about the foundational element shared by all vector spaces.
Question 2
True or False: Any linear combination of vectors in a subspace will result in a vector that is also in the subspace.
- True
- False
💡 Hint: Consider the definition of span.
Solve and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Given vectors (2, 3) and (4, 6) in R², determine if their span forms a subspace of R².
💡 Hint: Check if the vectors are linearly independent or dependent.
Question 2
Demonstrate if the intersection of two lines in R² is a subspace.
💡 Hint: Consider different conditions under which the lines may or may not intersect.
Challenge and get performance evaluation