Practice - Subspaces
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Practice Questions
Test your understanding with targeted questions
What are the three conditions for a subset to be a subspace?
💡 Hint: Think about the defining properties of a vector space.
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.
4 more questions available
Interactive Quizzes
Quick quizzes to reinforce your learning
What is a requirement for a subset W to be a subspace of V?
💡 Hint: Think of the operations allowed within the vector space.
True or False: All lines in ℝ² are subspaces.
💡 Hint: Recall the specific properties of subspaces you've learned.
1 more question available
Challenge Problems
Push your limits with advanced challenges
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.
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.
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Reference links
Supplementary resources to enhance your learning experience.