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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Determine whether the vectors [1, 2] and [2, 4] are linearly independent.
💡 Hint: Check if one vector can be expressed as a multiple of the other.
Question 2
Easy
Is the set of vectors {[1, 0], [0, 1]} linearly independent?
💡 Hint: Visualize their placement on a graph.
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 the first step to determine if vectors are linearly independent using a matrix?
- A. Check their dot product
- B. Form a matrix with them as columns
- C. Look for scalar multiples
💡 Hint: Think about the initial setup in matrix terms.
Question 2
True or False: If the number of pivot columns equals the number of vectors, they are dependent.
- True
- False
💡 Hint: Recall the defining characteristics of dependence.
Solve and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Given the vectors A: [1, 2, 3], B: [4, 5, 6], and C: [7, 8, 9], determine if they are independent using row reduction.
💡 Hint: Look for identical rows during reduction.
Question 2
In R^3, analyze the vectors [1, 2, 3], [2, 4, 6], [1, 0, 0]. Is it possible for them to be independent?
💡 Hint: Check whether any vector can be generated from others.
Challenge and get performance evaluation