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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Define a linear transformation.
💡 Hint: Think about the properties involved in vector addition.
Question 2
Easy
What is the image of a linear transformation?
💡 Hint: What do we call the output set of a function?
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 linear transformation?
- A type of scalar multiplication
- A function between vector spaces preserving operations
- Any function mapping numbers
💡 Hint: Look back at how it preserves vector operations.
Question 2
True or False: The kernel of a linear transformation is always a subspace of the target vector space.
- True
- False
💡 Hint: Think about where the zero vector maps.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Given a linear transformation T: R² → R² represented by the matrix A = [[2, 0], [0, 3]], determine the image and kernel of T.
💡 Hint: Think about how matrix transformations affect the unit vectors.
Question 2
Consider the linear transformation T(x, y) = (x + y, x - y). Is T one-to-one? Justify your answer.
💡 Hint: Analyze the equations derived from setting T to zero.
Challenge and get performance evaluation