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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Determine if the set of vectors { (1,0), (0,1) } is linearly independent.
💡 Hint: Consider their geometric representation.
Question 2
Easy
Is the vector { (1,1), (1,1) } linearly independent?
💡 Hint: Look for redundancy in vectors.
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
True or False: A set of vectors is linearly independent if at least one vector can be expressed as a combination of others.
- True
- False
💡 Hint: Recall the definitions of independence and dependence.
Question 2
Which of the following sets of vectors are linearly dependent? {(1,0),(1,0)}, {(1,2),(2,4)}, or {(1,1),(1,-1)}?
- Set A
- Set B
- Set C
💡 Hint: Look for vectors that can be expressed in terms of each other.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Given the vectors {(1,2,3), (2,4,6), (3,6,9)}, demonstrate through matrix methods that they are dependent.
💡 Hint: Look at the ratios between the rows.
Question 2
In R^3, provide a set of four vectors and argue whether they can be independent or dependent.
💡 Hint: Recall dimensional limits in linear algebra.
Challenge and get performance evaluation