Professional Courses
Industry-relevant training in Business, Technology, and Design to help professionals and graduates upskill for real-world careers.
Categories
Interactive Games
Fun, engaging games to boost memory, math fluency, typing speed, and English skills—perfect for learners of all ages.
Typing
Memory
Math
English Adventures
Knowledge
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 related to the topic.
Question 1
Easy
Determine if the vectors v₁ = (1, 2) and v₂ = (-2, -4) are linearly independent.
💡 Hint: Look for a scalar multiple.
Question 2
Easy
Are the vectors v₁ = (0, 1) and v₂ = (1, 0) independent?
💡 Hint: Think about their directions.
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 can be expressed in terms of one another
- They cannot express the zero vector unless all coefficients are zero
- They always lie on the same line
💡 Hint: Think about how combinations of coefficients work.
Question 2
True or False: If one vector in a set can be expressed as a linear combination of the others, the set is linearly independent.
- True
- False
💡 Hint: Review the definitions of dependence and independence.
Solve and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Given the vectors (1,2,3), (2,4,6), and (3,6,9), demonstrate whether they are linearly independent or dependent. Prove your answer mathematically.
💡 Hint: Get the system of equations formed by their linear combination equating to zero.
Question 2
Take the vectors (1,0,0), (0,1,0), and (0,0,1). Show they span R³ and are independent.
💡 Hint: Try forming the identity matrix with these as columns.
Challenge and get performance evaluation