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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Determine whether the vectors (1, 1) and (2, 2) are linearly dependent.
💡 Hint: Look for scalar multiples.
Question 2
Easy
Are the vectors (1, 0) and (0, 1) linearly independent?
💡 Hint: Check if one can be created through 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 does it mean for vectors to be linearly dependent?
- They point in the same direction
- At least one can be expressed as a combination of others
- They are orthogonal
💡 Hint: Think of how many directions they actually span.
Question 2
True or False: A set of vectors can be both linearly dependent and independent at the same time.
- True
- False
💡 Hint: Consider the definitions.
Solve and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Given vectors v₁ = (1, 1, 1), v₂ = (2, 2, 2), and v₃ = (3, 3, 3), prove whether they are dependent or independent.
💡 Hint: Look for scalar relationships.
Question 2
Using the vectors u = (1, 2, 3), v = (4, 5, 6), and w = (7, 8, 9), find the conditions under which these can be independent.
💡 Hint: Matrix properties indicate independence.
Challenge and get performance evaluation