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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 what properties must hold for the transformation.
Question 2
Easy
What is the kernel of a linear transformation?
💡 Hint: Consider where the transformation takes vectors.
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 does a linear transformation preserve?
- Addition and scalar multiplication
- Only addition
- Only scalar multiplication
💡 Hint: Think about the properties of operations in vector spaces.
Question 2
True or False: The kernel of a transformation includes all vectors mapped to zero.
- True
- False
💡 Hint: Consider what it means to be mapped to zero.
Solve 2 more questions and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Given the linear transformation T(x, y) = (2x, 3y), determine the kernel and image.
💡 Hint: Evaluate what inputs lead to the zero output to find the kernel.
Question 2
If A is a 3x3 matrix with rank 2, what can be said about its nullity?
💡 Hint: Use the Rank-Nullity theorem as a guide for this question.
Challenge and get performance evaluation