23.1 - Vector Spaces and Basis (Recap)
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Practice Questions
Test your understanding with targeted questions
Define a vector space.
💡 Hint: Think about the operations you can perform within it.
What is a basis of a vector space?
💡 Hint: Consider the relationship between spanning and independence.
4 more questions available
Interactive Quizzes
Quick quizzes to reinforce your learning
What is a vector space?
💡 Hint: Remember the definition.
Is every basis a linearly independent set?
💡 Hint: Consider the definition of basis.
2 more questions available
Challenge Problems
Push your limits with advanced challenges
Consider the set of vectors A = {(1,2), (2,4), (3,6)}. Prove if A is linearly independent or dependent.
💡 Hint: Use the properties of scaling factors.
In a space R^4, you need to determine if the set { (1,0,0,0), (0,1,0,0), (0,0,1,0), (0,0,0,1), (1,1,1,1) } is independent.
💡 Hint: Consider the dimension relation.
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