Practice Composition Of Linear Transformations (28.6) - Linear Transformations

Practice: Composition of Linear Transformations

Lesson 28.6Linear Transformations

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8 questions

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6 sample questions

Question 1.
What is the composition of a linear transformation?
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Think about how you would sequence two different actions.
Question 2.
Write down the formula for composition of T1: U → V and T2: V → W.
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What comes first: T1 or T2?
3Question 3.
True or False: The composition of two linear transformations is always a linear transformation.
- True
- False
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Recall the definition of a linear transformation.
4Question 4.
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
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Think about matrix multiplication's order.
Question 5.
Given two transformations T1(x) = x + 1 and T2(x) = 2x, compute the composition T2 ∘ T1. What does this composition represent mathematically?
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Remember to substitute T1 into the expression for T2.
Question 6.
Prove that if T1 and T2 are linear transformations, then the composition T2 ∘ T1 is also linear by demonstrating it satisfies additivity and homogeneity.
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Use the linear properties of T1 and T2 individually to derive the conditions for T2 ∘ T1.

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