24.2 - Examples of Vector Spaces
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Practice Questions
Test your understanding with targeted questions
What is an n-tuple?
💡 Hint: Think of examples like (1, 2, 3) or (x, y).
Define closure property in the context of vector spaces.
💡 Hint: Consider addition of two vectors.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What does ℝⁿ represent?
💡 Hint: Consider what the notation implies about dimensions.
Are all real-valued functions a subset of vector spaces?
💡 Hint: Evaluate if functions can be added or scaled.
1 more question available
Challenge Problems
Push your limits with advanced challenges
Show that the set of all continuous real-valued functions forms a vector space.
💡 Hint: Consider the properties of continuity and addition.
Determine if the set { f(x) = x³, g(x) = 2x² } is a vector space under standard polynomial operations.
💡 Hint: Focus on the definition of polynomial spaces.
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