Practice - Linear Independence and Dependence
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Practice Questions
Test your understanding with targeted questions
Determine if the vectors v₁ = (1, 2) and v₂ = (-2, -4) are linearly independent.
💡 Hint: Look for a scalar multiple.
Are the vectors v₁ = (0, 1) and v₂ = (1, 0) independent?
💡 Hint: Think about their directions.
4 more questions available
Interactive Quizzes
Quick quizzes to reinforce your learning
What does it mean for a set of vectors to be linearly independent?
💡 Hint: Think about how combinations of coefficients work.
True or False: If one vector in a set can be expressed as a linear combination of the others, the set is linearly independent.
💡 Hint: Review the definitions of dependence and independence.
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Challenge Problems
Push your limits with advanced challenges
Given the vectors (1,2,3), (2,4,6), and (3,6,9), demonstrate whether they are linearly independent or dependent. Prove your answer mathematically.
💡 Hint: Get the system of equations formed by their linear combination equating to zero.
Take the vectors (1,0,0), (0,1,0), and (0,0,1). Show they span R³ and are independent.
💡 Hint: Try forming the identity matrix with these as columns.
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