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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Define what a basis is in the context of vector spaces.
💡 Hint: Consider how vectors relate to each other in terms of dependencies.
Question 2
Easy
What is the dimension of R⁵?
💡 Hint: Think about how many independent directions are in the space.
Practice 4 more questions and get performance evaluation
Interactive Quizzes
Engage in quick quizzes to reinforce what you've learned and check your comprehension.
Question 1
What is a basis of a vector space?
- A set of vectors that are not independent.
- A linearly independent set of vectors that spans the space.
- Any set of vectors in the vector space.
💡 Hint: Think about the criteria a set must meet to be considered a basis.
Question 2
Does the zero vector space have a basis?
- True
- False
💡 Hint: Consider how many independent vectors are necessary for a basis.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
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.
Question 2
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.
Challenge and get performance evaluation