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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Define a linear transformation in your own words.
💡 Hint: Focus on what happens with vector addition.
Question 2
Easy
What is the kernel of a linear transformation?
💡 Hint: Think of the output of the transformation.
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 definition of a linear transformation?
💡 Hint: Remember the vector space properties.
Question 2
True or False: The kernel of a linear transformation includes all vectors mapped to the zero vector.
- True
- False
💡 Hint: Think about how 'zero' is represented in transformations.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
A linear transformation T: R^2 to R^2 is defined by T(x, y) = (3x + y, 2x - y). Calculate the kernel and the range of T.
💡 Hint: Complement approaches using systems of equations.
Question 2
In a transformation defined by a matrix A = [[1, 0], [0, 2]] mapping R^2, analyze how the dimension changes when restricting the mapping to a line.
💡 Hint: Draw diagrams if necessary to visualize transformations.
Challenge and get performance evaluation