21.14 - Linear Transformations
Enroll to start learning
You’ve not yet enrolled in this course. Please enroll for free to listen to audio lessons, classroom podcasts and take practice test.
Practice Questions
Test your understanding with targeted questions
Define a linear transformation in your own words.
💡 Hint: Focus on what happens with vector addition.
What is the kernel of a linear transformation?
💡 Hint: Think of the output of the transformation.
4 more questions available
Interactive Quizzes
Quick quizzes to reinforce your learning
What is the definition of a linear transformation?
💡 Hint: Remember the vector space properties.
True or False: The kernel of a linear transformation includes all vectors mapped to the zero vector.
💡 Hint: Think about how 'zero' is represented in transformations.
1 more question available
Challenge Problems
Push your limits with advanced challenges
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.
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.
Get performance evaluation
Reference links
Supplementary resources to enhance your learning experience.