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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Define the kernel of a linear transformation.
💡 Hint: Think about what happens when you apply T to some vectors.
Question 2
Easy
What is the range of a linear transformation?
💡 Hint: Consider all possible images that can be created from a set of inputs.
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 kernel of a linear transformation?
💡 Hint: Think about what inputs give zero outputs in the transformation.
Question 2
True or False: The range of a linear transformation can be larger than the codomain.
- True
- False
💡 Hint: Consider the relationship between outputs and the broader space.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Given the matrix A = [[1, 2], [3, 4]], analyze the kernel and range. Determine if the transformation is injective.
💡 Hint: Consider both null space and image through operations on matrix A.
Question 2
If the transformation T represented by a 4x3 matrix has a kernel dimension of 1, what is the maximum rank of this transformation?
💡 Hint: Apply the theorem to deduce the rank from given dimensions.
Challenge and get performance evaluation