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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What is the composition of a linear transformation?
💡 Hint: Think about how you would sequence two different actions.
Question 2
Easy
Write down the formula for composition of T1: U → V and T2: V → W.
💡 Hint: What comes first: T1 or T2?
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
True or False: The composition of two linear transformations is always a linear transformation.
- True
- False
💡 Hint: Recall the definition of a linear transformation.
Question 2
What is the representation of the composition of T1 and T2 if A is the matrix of T1 and B is the matrix of T2?
- AB
- BA
- A+B
💡 Hint: Think about matrix multiplication's order.
Solve and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Given two transformations T1(x) = x + 1 and T2(x) = 2x, compute the composition T2 ∘ T1. What does this composition represent mathematically?
💡 Hint: Remember to substitute T1 into the expression for T2.
Question 2
Prove that if T1 and T2 are linear transformations, then the composition T2 ∘ T1 is also linear by demonstrating it satisfies additivity and homogeneity.
💡 Hint: Use the linear properties of T1 and T2 individually to derive the conditions for T2 ∘ T1.
Challenge and get performance evaluation