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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Are the vectors [1, 0] and [0, 1] in R² linearly independent?
💡 Hint: Consider their geometric representation.
Question 2
Easy
Determine if the vectors [1, 1] and [1, 2] are linearly independent.
💡 Hint: Look for a solution for coefficients that results in zero.
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 a set of vectors to be linearly independent?
- They span the same space.
- They can be combined to give zero with non-zero solutions.
- Their linear combination results in zero only with all coefficients being zero.
💡 Hint: Recall the definition given in class.
Question 2
Is the set containing the zero vector linearly dependent?
- True
- False
💡 Hint: Consider the implications of the zero vector.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Prove that the vectors (1, 1, 1), (2, 2, 2), (3, 3, 3) are linearly dependent by showing how one vector is a linear combination of the others.
💡 Hint: Set up the equation and solve using coefficient comparison.
Question 2
Given vectors (1, 0) and (a, b) in R², find conditions on a and b for independence.
💡 Hint: Use the determinant condition for independence.
Challenge and get performance evaluation