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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Identify if the vectors (1, 2) and (3, 6) are independent or dependent.
💡 Hint: Look for scalar multiples.
Question 2
Easy
Are the vectors (2,1) and (1,-2) independent?
💡 Hint: Check if you can express one in terms of the other.
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 characterizes a set of linearly independent vectors?
- They can form the zero vector only with zero coefficients
- They can be expressed as linear combinations of others
- They span the entire vector space
💡 Hint: Think about what it means for vectors to combine to zero.
Question 2
True or False: The vectors (1, 2) and (2, 4) are linearly independent.
- True
- False
💡 Hint: Check if one vector is a multiplier of the other.
Solve and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Prove that the vectors (2, 3) and (2, 6) are dependent by showing a scalar relationship.
💡 Hint: Form a linear combination to see if you can make zero.
Question 2
Given vectors (3, 1) and (1, 3), find a linear combination that shows they are independent or dependent.
💡 Hint: Try setting up the equation with scalars to see if it leads to a solution.
Challenge and get performance evaluation