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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Define linear dependence.
💡 Hint: Think of whether one vector can be formed with the others.
Question 2
Easy
What is linear independence?
💡 Hint: Remember, the scalars must all be zero.
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 defines linear dependence?
- A vector can stand alone.
- One vector can be expressed as a combination of others.
- All vectors are independent.
💡 Hint: Think about how vectors relate to each other.
Question 2
True or False: The vector set { (1, 2), (2, 4) } is linearly independent.
- True
- False
💡 Hint: Check if one vector can be made by combining others.
Solve and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Consider the vectors v1 = (1, 2, 3), v2 = (2, 4, 6), and v3 = (3, 6, 9). Are these vectors linearly dependent or independent? Justify your answer.
💡 Hint: Look for constants that can express one vector through another.
Question 2
An engineer decides to remove redundant structural supports based on vector analysis. If the original supports were based on vectors that are dependent, how would this affect the safety of the structure?
💡 Hint: Re-evaluate the role each support plays in load-bearing.
Challenge and get performance evaluation