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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Determine if the vectors [1, 0] and [0, 1] are linearly independent.
💡 Hint: Check if you can form one vector from the other.
Question 2
Easy
Using the Wronskian, test the independence of functions f(x) = e^x and g(x) = e^(2x).
💡 Hint: Calculate the determinant of the matrix formed by the functions and their derivatives.
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 the criterion for vectors in Rn to be linearly independent?
- Row reduced matrix must have full rank
- Vectors must be orthogonal
- Vectors cannot be identical
💡 Hint: Think about what rank implies for the set of vectors.
Question 2
Is the Wronskian used for functions or vectors?
- True
- False
💡 Hint: Recall the definition of the Wronskian.
Solve and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Given vectors v1 = [1, 2, 3], v2 = [2, 4, 6], and v3 = [1, 0, 1], determine if they form a basis for R3.
💡 Hint: Use row reduction to analyze their relationships.
Question 2
For the functions f(x) = x and g(x) = x^2, calculate the Wronskian and describe their independence.
💡 Hint: Perform the determinant calculation for completeness.
Challenge and get performance evaluation