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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Determine if the following vectors are linearly dependent: (2,4), (1,2), (3,6)
💡 Hint: Look for scalar multiples.
Question 2
Easy
Are the vectors (1, 1) and (1, -1) linearly independent?
💡 Hint: Set up the equation and solve.
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 defines linear dependence among vectors?
- A unique solution exists
- Multiple solutions exist
- Only one vector can be expressed as a combination of others
💡 Hint: Think in terms of solutions to linear equations.
Question 2
True or False: If only linear combinations of zeros result in the zero vector, the vectors are linearly independent.
- True
- False
💡 Hint: Recall the definitions of dependence versus independence.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
In 3D space, consider vectors A = (1, 0, 0), B = (0, 1, 0), and C = (0, 0, 1). Are these vectors dependent or independent? Justify your answer with a general linear combination.
💡 Hint: Use the definition of independence for validation.
Question 2
Given the vectors D = (1, 2, 3), E = (2, 4, 6), and F = (1, 1, 1), determine if the set is dependent or independent and explain.
💡 Hint: Check for scalar multiples and linear combinations.
Challenge and get performance evaluation