Practice Linear Transformations (21.14) - Linear Algebra

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9 questions

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Exercise
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6 sample questions

Question 1.
Define a linear transformation in your own words.
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Focus on what happens with vector addition.
Question 2.
What is the kernel of a linear transformation?
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Think of the output of the transformation.
3Question 3.
What is the definition of a linear transformation?
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Remember the vector space properties.
4Question 4.
True or False: The kernel of a linear transformation includes all vectors mapped to the zero vector.
- True
- False
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Think about how 'zero' is represented in transformations.
Question 5.
A linear transformation T: R^2 to R^2 is defined by T(x, y) = (3x + y, 2x - y). Calculate the kernel and the range of T.
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Complement approaches using systems of equations.
Question 6.
In a transformation defined by a matrix A = [[1, 0], [0, 2]] mapping R^2, analyze how the dimension changes when restricting the mapping to a line.
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Draw diagrams if necessary to visualize transformations.

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