10. In one of the videos from the discussion thread, it talked about doing a transformation T: R² → R² defined by T(x) = Ax for A = [0.5 0.5 a. Demonstrate this transformation by applying it to a square. Draw a graph with the original square and the transformed square plotted. b. I want to know how this transformation affects the area of the shape. I want to answer this question in general, like "the transformation will multiply the area by 100." I can think of at least two ways to accomplish this: one having to do with elementary matrices, and one having to do with the eigenvalue/eigenvector problem. Answer the question for me and explain why your method works.

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Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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In one of the videos from the discussion thread, it talked about doing a transformation
T:R? → R² defined by T(x) = Ax for A = |ö5 05.
10.
1
-0.5 0.5
a. Demonstrate this transformation by applying it to a square. Draw a graph with the
original square and the transformed square plotted.
b. I want to know how this transformation affects the area of the shape. I want to answer
this question in general, like "the transformation will multiply the area by 100." I can
think of at least two ways to accomplish this: one having to do with elementary
matrices, and one having to do with the eigenvalue/eigenvector problem. Answer the
question for me and explain why your method works.
Transcribed Image Text:In one of the videos from the discussion thread, it talked about doing a transformation T:R? → R² defined by T(x) = Ax for A = |ö5 05. 10. 1 -0.5 0.5 a. Demonstrate this transformation by applying it to a square. Draw a graph with the original square and the transformed square plotted. b. I want to know how this transformation affects the area of the shape. I want to answer this question in general, like "the transformation will multiply the area by 100." I can think of at least two ways to accomplish this: one having to do with elementary matrices, and one having to do with the eigenvalue/eigenvector problem. Answer the question for me and explain why your method works.
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