21.8.2 - Subspace
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Practice Questions
Test your understanding with targeted questions
Define a subspace in your own words.
💡 Hint: Think about closure under operations.
What is meant by the basis of a subspace?
💡 Hint: Consider how you can represent all vectors in the subspace.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is a subspace?
💡 Hint: Think about properties shared with the original space.
True or False: Every subset of a vector space is a subspace.
💡 Hint: Consider the criteria for being a subspace.
1 more question available
Challenge Problems
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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.
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.
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