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21-02-2024
Mathematics

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Let u and v be vectors in R n . It can be shown that the set P of all points in the parallelogram determined by u and v has the form au C bv, for 0 a 1, 0 b 1. Let T W R n ! R m be a linear transformation. Explain why the image of a point in P under the transformation T lies in the parallelogram determined by T .u/ and T .v/.

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