24 - Vector Space
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Practice Questions
Test your understanding with targeted questions
Define a vector space and its basic properties.
💡 Hint: Think about operations and the necessary rules that govern them.
What is a subspace? Give an example.
💡 Hint: Recall the properties that validate a subspace.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is a vector space?
💡 Hint: Recall the operations that define a vector space.
True or False: A subspace can include only some of the vectors in a vector space.
💡 Hint: Think about the properties that define a subspace.
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Challenge Problems
Push your limits with advanced challenges
Find and prove a basis for the vector space spanned by the vectors (3, 6) and (1, 2).
💡 Hint: Consider how one vector can be formed from the other.
Prove that the set W = {(x, y, z) ∈ R^3 | x + 2y + 3z = 0} is a subspace of R^3.
💡 Hint: You need to satisfy all three conditions for subspaces.
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