26.6 - Basis and Dimension
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Practice Questions
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Define what a basis is in the context of vector spaces.
💡 Hint: Consider how vectors relate to each other in terms of dependencies.
What is the dimension of R⁵?
💡 Hint: Think about how many independent directions are in the space.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is a basis of a vector space?
💡 Hint: Think about the criteria a set must meet to be considered a basis.
Does the zero vector space have a basis?
💡 Hint: Consider how many independent vectors are necessary for a basis.
1 more question available
Challenge Problems
Push your limits with advanced challenges
Given a vector space consisting of vectors in R³, determine if the set {(1,0,0), (0,1,0), (0,0,1), (1,1,1)} is a basis. Explain your reasoning.
💡 Hint: Check if the last vector can be formed using coefficients from the first three.
If a vector space V has dimension n, show that no more than n vectors can be linearly independent in V.
💡 Hint: Consider how adding vectors beyond the dimension interacts with independence.
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