21.8 - Vector Spaces and Subspaces
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Practice Questions
Test your understanding with targeted questions
Define a vector space.
💡 Hint: Think about the operations we perform on vectors.
What is a subspace?
💡 Hint: What must the subset satisfy?
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is a vector space?
💡 Hint: Think about what defines a vector space.
Is a subspace a vector space?
💡 Hint: Recall what a subset must satisfy.
1 more question available
Challenge Problems
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Given three vectors in R^3, determine if they form a basis. Show your calculations.
💡 Hint: Use row reduction to check for independence.
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?
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