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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What is a basis in vector space?
💡 Hint: Think about how vectors can represent points in space.
Question 2
Easy
How is the dimension of a vector space determined?
💡 Hint: Consider how many directions can be formed by the basis vectors.
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 in linear algebra?
- A set of all vectors in a space
- A set of linearly independent vectors that span the space
- A vector that does not change direction
💡 Hint: Remember the definition of linear combinations.
Question 2
Dimension refers to:
- True
- False
💡 Hint: Think of how many directions the basis can point.
Solve 2 more questions and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Determine if the vectors (3,1,2), (2,0,0), and (0,4,1) are linearly independent. What is the dimension of their span?
💡 Hint: Try arranging the vectors into a matrix to examine their independence.
Question 2
Given a vector space of dimension 5, what are possible bases for it, and how would you verify their independence?
💡 Hint: Consider the geometric interpretation of vector directions.
Challenge and get performance evaluation