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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What is the formula for the norm of a vector in an inner product space?
💡 Hint: Recall how the inner product is used to determine the norm.
Question 2
Easy
Is the norm ever negative? Why or why not?
💡 Hint: Think about the properties of lengths or distances.
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 norm of a vector defined as?
- The inner product of the vector with itself
- The outer product of the vector
- The sum of components of the vector
💡 Hint: Think about how we calculate the distance or length.
Question 2
True or False: The norm of a vector can be negative.
- True
- False
💡 Hint: What do you know about lengths?
Solve and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Given vector a = (3, 4) and b = (1, 2), calculate the distance between these two vectors using their norms.
💡 Hint: Remember that distance can be found using the norm of the difference between the vectors.
Question 2
Prove that the norms behave correctly under scalar multiplication by showing how ∥2v∥ relates to ∥v∥.
💡 Hint: Use the definition of the norm with the inner product to show this relationship.
Challenge and get performance evaluation