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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 inputs lead to zero outputs.
Question 2
Easy
What is the range of a linear transformation?
💡 Hint: Consider the images of all input vectors.
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 inputs that cause no change.
Question 2
The range of T is the set of all vectors mapped to [0] in the codomain. True or False?
💡 Hint: Focus on the outputs of the transformation.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Given a linear transformation T: R^3 → R^3 defined by T(x, y, z) = (x + y - z, 2y, -x + z), find the kernel and range.
💡 Hint: Use matrix representation if necessary to analyze.
Question 2
How does a change in dimension of the kernel affect the system of equations represented in a transformation?
💡 Hint: Relate to the implications of the Rank-Nullity theorem.
Challenge and get performance evaluation