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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Define a vector space.
💡 Hint: Think about the operations you can perform within it.
Question 2
Easy
What is a basis of a vector space?
💡 Hint: Consider the relationship between spanning and independence.
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 vector space?
- A collection of vectors unable to add
- A closed set under addition and scalar multiplication
- Any collection of numbers
💡 Hint: Remember the definition.
Question 2
Is every basis a linearly independent set?
- True
- False
💡 Hint: Consider the definition of basis.
Solve 2 more questions and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
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.
Question 2
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.
Challenge and get performance evaluation