Practice Linear Transformations (26.11) - Vector Spaces - Mathematics (Civil Engineering -1)

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9 questions

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6 sample questions

Question 1.
Define a linear transformation.
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Think about the properties involved in vector addition.
Question 2.
What is the image of a linear transformation?
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What do we call the output set of a function?
3Question 3.
What is a linear transformation?
- A type of scalar multiplication
- A function between vector spaces preserving operations
- Any function mapping numbers
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Look back at how it preserves vector operations.
4Question 4.
True or False: The kernel of a linear transformation is always a subspace of the target vector space.
- True
- False
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Think about where the zero vector maps.
Question 5.
Given a linear transformation T: R² → R² represented by the matrix A = [[2, 0], [0, 3]], determine the image and kernel of T.
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Think about how matrix transformations affect the unit vectors.
Question 6.
Consider the linear transformation T(x, y) = (x + y, x - y). Is T one-to-one? Justify your answer.
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Analyze the equations derived from setting T to zero.

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