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
What are the two properties of a linear transformation?
💡 Hint: Think of how the transformation interacts with vector addition and scalar multiplication.
Question 2
Easy
Is the function T(x) = 3x a linear transformation? Why?
💡 Hint: Check the properties with addition and scalar multiplication.
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
Which of the following properties is NOT satisfied by linear transformations?
- Additivity
- Homogeneity
- Non-linearity
💡 Hint: Remember the two fundamental properties!
Question 2
True or False: The zero transformation is a type of linear transformation.
- True
- False
💡 Hint: Does it meet the linear transformation criteria?
Solve and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Prove that the transformation T: R^2 → R^2 defined by T(x, y) = (2x, 3y) is linear.
💡 Hint: Use arbitrary u = (u1, u2) and v = (v1, v2) to simplify your proof.
Question 2
Demonstrate that the transformation T given by T(x) = 5x + 2 is NOT linear.
💡 Hint: Examine what happens with the constant addition of 2.
Challenge and get performance evaluation