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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Determine if the set { [1, 0], [0, 1], [1, 1] } is linearly independent.
💡 Hint: Look for combinations of vectors that produce another vector in the set.
Question 2
Easy
Is the set { [0, 0], [1, 1] } linearly independent?
💡 Hint: Remember the importance of the zero vector.
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
A set containing the zero vector is linearly dependent.
- True
- False
💡 Hint: Consider what the zero vector represents in a linear combination.
Question 2
In R^4, a set of five vectors must be linearly independent.
- True
- False
💡 Hint: Reflect on the dimensionality of R^n.
Solve 2 more questions and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Prove that the three vectors v1 = (1,0,0), v2 = (0,1,0), v3 = (0,0,1) are linearly independent.
💡 Hint: You can set up a matrix and check its rank or use geometric reasoning.
Question 2
Consider the vectors u1 = (1,1,0), u2 = (2,2,0), u3 = (0,3,0). Are these vectors linearly independent? Justify your answer.
💡 Hint: Check if any vector is a linear combination of the others.
Challenge and get performance evaluation