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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Define a subspace in your own words.
💡 Hint: Think about closure under operations.
Question 2
Easy
What is meant by the basis of a subspace?
💡 Hint: Consider how you can represent all vectors in the subspace.
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 subspace?
- A larger space than a vector space
- A subset of a vector space that is itself a vector space
- A collection of all the linear transformations
💡 Hint: Think about properties shared with the original space.
Question 2
True or False: Every subset of a vector space is a subspace.
- True
- False
💡 Hint: Consider the criteria for being a subspace.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Given the vectors (1, 2, 3) and (2, 4, 6), determine if they form a basis for R³ and justify why or why not.
💡 Hint: Consider the independence of these vectors.
Question 2
Prove that the set of all vectors in R² that can be expressed as (x, 0) for any real number x forms a subspace.
💡 Hint: Check that adding any two such vectors still results in a vector of the same form.
Challenge and get performance evaluation