Practice - Examples
Enroll to start learning
You’ve not yet enrolled in this course. Please enroll for free to listen to audio lessons, classroom podcasts and take practice test.
Practice Questions
Test your understanding with targeted questions
Are the vectors [2, 1], [4, 2] linearly independent?
💡 Hint: Check if one vector can be expressed as a scalar multiple of another.
Is the set {(1, 0), (0, 1)} linearly independent?
💡 Hint: Consider the geometric representation of these vectors.
4 more questions available
Interactive Quizzes
Quick quizzes to reinforce your learning
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.
Is the following statement true or false? 'Three vectors can be linearly independent in a 2-D space.'
💡 Hint: Consider the dimensionality of the space.
Get performance evaluation
Challenge Problems
Push your limits with advanced challenges
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.
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.
Get performance evaluation
Reference links
Supplementary resources to enhance your learning experience.