28.6 - Composition of Linear Transformations
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Practice Questions
Test your understanding with targeted questions
What is the composition of a linear transformation?
💡 Hint: Think about how you would sequence two different actions.
Write down the formula for composition of T1: U → V and T2: V → W.
💡 Hint: What comes first: T1 or T2?
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Interactive Quizzes
Quick quizzes to reinforce your learning
True or False: The composition of two linear transformations is always a linear transformation.
💡 Hint: Recall the definition of a linear transformation.
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?
💡 Hint: Think about matrix multiplication's order.
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Challenge Problems
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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.
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.
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