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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What is a basis in a vector space?
💡 Hint: Think about the minimal number of vectors needed to describe all vectors in the space.
Question 2
Easy
Give an example of a basis for R².
💡 Hint: Consider the axes in a two-dimensional 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 single vector
- A set of vectors
- A linearly dependent set
💡 Hint: Remember the properties that define a basis.
Question 2
True or False: The vectors (1,2) and (1,2) can form a basis for R².
- True
- False
💡 Hint: Consider if the vectors can be combined to give you the identity vector.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Find a basis for the vector space spanned by the vectors {(2,4), (-1,-2), (3,6)}.
💡 Hint: Identify which vectors are linearly dependent.
Question 2
Determine if the set {(1,1), (2,2), (3,4)} is a basis for R². Explain your reasoning.
💡 Hint: Try expressing one vector as a combination of others.
Challenge and get performance evaluation