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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 we perform on vectors.
Question 2
Easy
What is a subspace?
💡 Hint: What must the subset satisfy?
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 set without operations
- A set of objects
- A set of vectors closed under addition and scalar multiplication
💡 Hint: Think about what defines a vector space.
Question 2
Is a subspace a vector space?
- True
- False
💡 Hint: Recall what a subset must satisfy.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Given three vectors in R^3, determine if they form a basis. Show your calculations.
💡 Hint: Use row reduction to check for independence.
Question 2
You have a vector space of dimension 5. If you remove one vector that is part of the basis, what happens to the dimension? Explain your reasoning.
💡 Hint: How do basis vectors relate to the definition of dimension?
Challenge and get performance evaluation