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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 the defining properties of a vector space.
Question 2
Easy
Is the set of vectors { (1,0), (0,1), (1,1) } a subspace of ℝ²?
💡 Hint: Verify if zero vector is included and if adding two members gives another member.
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 requirement for a subset W to be a subspace of V?
- It must contain at least two vectors
- It must be closed under vector addition
- It must not include the zero vector
💡 Hint: Think of the operations allowed within the vector space.
Question 2
True or False: All lines in ℝ² are subspaces.
- True
- False
💡 Hint: Recall the specific properties of subspaces you've learned.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Prove that the span of any set of vectors is a subspace.
💡 Hint: Start by considering what happens when you combine vectors in the span.
Question 2
Find two vectors in ℝ² that form a line through the origin and demonstrate the closure properties.
💡 Hint: Visualize this on a graph for clarity.
Challenge and get performance evaluation