Practice Linear Independence - 24.5 | 24. Vector Space | Mathematics (Civil Engineering -1)
Students

Academic Programs

AI-powered learning for grades 8-12, aligned with major curricula

Professional

Professional Courses

Industry-relevant training in Business, Technology, and Design

Games

Interactive Games

Fun games to boost memory, math, typing, and English skills

Linear Independence

24.5 - Linear Independence

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.

Learning

Practice Questions

Test your understanding with targeted questions

Question 1 Easy

Identify if the vectors (1, 2) and (3, 6) are independent or dependent.

💡 Hint: Look for scalar multiples.

Question 2 Easy

Are the vectors (2,1) and (1,-2) independent?

💡 Hint: Check if you can express one in terms of the other.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What characterizes a set of linearly independent vectors?

They can form the zero vector only with zero coefficients
They can be expressed as linear combinations of others
They span the entire vector space

💡 Hint: Think about what it means for vectors to combine to zero.

Question 2

True or False: The vectors (1, 2) and (2, 4) are linearly independent.

True
False

💡 Hint: Check if one vector is a multiplier of the other.

Get performance evaluation

Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Prove that the vectors (2, 3) and (2, 6) are dependent by showing a scalar relationship.

💡 Hint: Form a linear combination to see if you can make zero.

Challenge 2 Hard

Given vectors (3, 1) and (1, 3), find a linear combination that shows they are independent or dependent.

💡 Hint: Try setting up the equation with scalars to see if it leads to a solution.

Get performance evaluation

Reference links

Supplementary resources to enhance your learning experience.