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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Identify if the functions 1, x, x² are linearly independent.
💡 Hint: Consider their definitions and how they relate.
Question 2
Easy
Give an example of two linearly dependent functions.
💡 Hint: Look for functions that can create each other.
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 sets of functions is linearly independent?
- {1
- x}
- {x
- 2x}
- {2x
- x²}
💡 Hint: Think about relations between the functions.
Question 2
True or False: All polynomial functions are linearly independent.
- True
- False
💡 Hint: Check relationships between polynomials.
Solve and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Given the functions f1(x) = e^x, f2(x) = e^(2x), and f3(x) = sin(x), determine if they are linearly independent.
💡 Hint: Use the Wronskian to check their independence.
Question 2
In structural dynamics, if a certain mode shape is found to be linearly dependent on others in a system of vibrations, what potential issues could arise?
💡 Hint: Consider the implications of redundancy in engineering designs.
Challenge and get performance evaluation