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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Define a vector space and its basic properties.
💡 Hint: Think about operations and the necessary rules that govern them.
Question 2
Easy
What is a subspace? Give an example.
💡 Hint: Recall the properties that validate a subspace.
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 vector space?
- A structure with addition and multiplication
- Only a set of numbers
- Any collection of points
💡 Hint: Recall the operations that define a vector space.
Question 2
True or False: A subspace can include only some of the vectors in a vector space.
- True
- False
💡 Hint: Think about the properties that define a subspace.
Solve and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Find and prove a basis for the vector space spanned by the vectors (3, 6) and (1, 2).
💡 Hint: Consider how one vector can be formed from the other.
Question 2
Prove that the set W = {(x, y, z) ∈ R^3 | x + 2y + 3z = 0} is a subspace of R^3.
💡 Hint: You need to satisfy all three conditions for subspaces.
Challenge and get performance evaluation