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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Are the vectors [2, 1], [4, 2] linearly independent?
💡 Hint: Check if one vector can be expressed as a scalar multiple of another.
Question 2
Easy
Is the set {(1, 0), (0, 1)} linearly independent?
💡 Hint: Consider the geometric representation of these 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
If a set of three vectors in R3 is dependent, what can be said about their relationships?
💡 Hint: Recall the definitions of linear independence and dependence.
Question 2
Is the following statement true or false? 'Three vectors can be linearly independent in a 2-D space.'
- True
- False
💡 Hint: Consider the dimensionality of the space.
Solve and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Given the vectors [2, 3, 1], [4, 6, 2], [5, 7, 4], determine if they are linearly independent or dependent and explain your reasoning.
💡 Hint: Form a matrix and use row reduction.
Question 2
Using the vectors (1, 2, -1), (2, 4, 2), (3, 6, 3), show they are dependent and find the relationship between them.
💡 Hint: Look for a common scalar that relates the vectors.
Challenge and get performance evaluation