28 - Linear Transformations
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Practice Questions
Test your understanding with targeted questions
Define a linear transformation.
💡 Hint: Think about what properties must hold for the transformation.
What is the kernel of a linear transformation?
💡 Hint: Consider where the transformation takes vectors.
4 more questions available
Interactive Quizzes
Quick quizzes to reinforce your learning
What does a linear transformation preserve?
💡 Hint: Think about the properties of operations in vector spaces.
True or False: The kernel of a transformation includes all vectors mapped to zero.
💡 Hint: Consider what it means to be mapped to zero.
2 more questions available
Challenge Problems
Push your limits with advanced challenges
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.
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.
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