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 defines a homogeneous system of equations?
💡 Hint: Consider the form of the system.
Question 2
Easy
What is the trivial solution to a homogeneous system?
💡 Hint: Think about the simplest solution.
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 is a homogeneous system of linear equations?
- A system where Ax = 0
- A system where b ≠ 0
- A system with unique solutions
💡 Hint: Recall the definition we discussed.
Question 2
True or False: The trivial solution of a homogeneous system is x = 1.
- True
- False
💡 Hint: Think about the simplest solution again.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Given a 3x3 matrix A with rows that are linearly dependent, find the null space of A and discuss the implications on the solutions of Ax = 0.
💡 Hint: Look for combinations of rows that demonstrate linear dependency.
Question 2
If a homogeneous system Ax = 0 has three variables and the rank of A is 1, describe the geometric interpretation of the solution space.
💡 Hint: Draw the axes and think about which direction represents the span of the solution.
Challenge and get performance evaluation