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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Define what a vector is.
💡 Hint: Think about how it appears graphically.
Question 2
Easy
What is a subspace?
💡 Hint: Consider if it contains the origin.
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 does the null space consist of?
- A set of all vectors in ℝ²
- Vectors mapped to the zero vector
- Vectors corresponding to the basis
💡 Hint: Remember its relationship to zero.
Question 2
True or False: A basis can include linearly dependent vectors.
- True
- False
💡 Hint: What does 'independent' mean in this context?
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Given a set of vectors in ℝ³, determine the basis and visualize it in a diagram.
💡 Hint: Focus on independence and dimensionality.
Question 2
Explain how to construct a null space given a specific transformation matrix.
💡 Hint: Sum things up to zero!
Challenge and get performance evaluation