46_hwc1SolnsODDA

46_hwc1SolnsODDA - 1 ² then we would have | ab-cd | = 1 so this would be an example of an area preserving matrix 6.7 Let A = h 1 2 3 4 i By the

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and you can now easily graph it. 6.5 Which, if either, of the following matrices corresponds to an area preserving transformation? A = h 2 - 3 1 3 i B = h 2 - 3 1 3 i . SOLUTION We compute the magnification factor for each of these matrices, and see whether it is 1 or not. By Theorem 16, the magnification factor of ± a b c d ² is | ab - cd | . Computing | ab - cd | for A we find 9, so A is not area preserving. As written, B is the same, so it is not area preserving. If however, we had B = ± 2 3 1
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Unformatted text preview: 1 ² , then we would have | ab-cd | = 1, so this would be an example of an area preserving matrix. 6.7 Let A = h 1 2 3 4 i . By the results of problem 1.6.6, the image of the unit circle under A is an ellipse. Find the equation of the ellipse and graph it. SOLUTION By the results of the previous problem, the equation of the ellipse is 25 u 2 + 5 v 2-22 uv = 4 . 21 /september/ 2005; 22:09 47...
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This note was uploaded on 10/03/2010 for the course MATH 380 taught by Professor Gladue during the Fall '08 term at Roger Williams.

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