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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Write a linear combination of the vectors (1, 2) and (3, 4).
💡 Hint: Use coefficients of your choice.
Question 2
Easy
What is the span of the vectors (1, 0) and (0, 1)?
💡 Hint: Think about what combinations can result from these 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 linear combination?
💡 Hint: Consider expressions of the form a1v1 + a2v2.
Question 2
True or False: The span of vectors is the collection of all linear combinations of those vectors.
- True
- False
💡 Hint: Remember definitions covered earlier.
Solve and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Given the vectors v1 = (1, 1) and v2 = (2, 2), find a unique combination resulting in the vector (3, 3). Discuss whether these two vectors are independent.
💡 Hint: Draw or graph these vectors to visually speculate about their relationship.
Question 2
Design a three-dimensional span using two specific non-parallel vectors. Discuss if it can fill the entire space.
💡 Hint: Visualize using a 3D graph to see how dimensions interact!
Challenge and get performance evaluation