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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What is a linear transformation?
💡 Hint: Think about how vectors behave under addition.
Question 2
Easy
Define the kernel of a linear transformation.
💡 Hint: Focus on what happens to vectors in the mapping.
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 only
- Scalar multiplication only
- Both addition and scalar multiplication
💡 Hint: Look back at the properties defined.
Question 2
True or False: The kernel of a linear transformation is the set of all vectors mapped to zero.
- True
- False
💡 Hint: Remember the definition of kernel.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Given the linear transformation T: R^3 → R^3 represented by the matrix [[1, 2, 3], [0, 1, 4], [0, 0, 0]], determine the kernel of this transformation.
💡 Hint: Set up the equation involving your transformation matrix and find when it results in the zero vector.
Question 2
If a linear transformation has a rank of 2 and operates on a 4-dimensional space, what is the dimension of the kernel?
💡 Hint: Remember the rank-nullity theorem connects dimensions; you have the rank and domain.
Challenge and get performance evaluation