MIT18_024S11_Pset3

MIT18_024S11_Pset3 - take any derivatives). You can justify...

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PSET 3 - DUE FEBRUARY 24 Note the date change for this Pset! Due Thursday at 11:00 a.m., before class. 1. Let T : R n R n be a linear transformation and let P denote a paralellpiped in R n formed by the vectors { v 1 , ··· ,v n } . Let m ( T ) denote the matrix of the transformation of T using the standard basis in R n . Finally, let T ( P ) denote the image of the parallelpiped under the transformation T . Prove vol ( T ( P )) = | det ( m ( T )) | vol ( P ) . (5 pts) 2. 14.4: 23 (5 pts) 3. Let P represent the plane containing the points (1 , 0 , 0) , (3 , 2 , 4) , (1 , 1 , 1). Find the point on the plane that minimizes the distance between the plane and the origin. Remark: You should solve this problem without using an optimization technique (don’t
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Unformatted text preview: take any derivatives). You can justify this point minimizes distance using the geometry of vectors. (5 pts) 4. 14.9:12 (5 pts) 5. 14.9:15 (5 pts) 6. 14.13:16 (5 pts) The problems from Chapter 14 refer to Apostol Volume I. 1 MIT OpenCourseWare http://ocw.mit.edu 18.024 Multivariable Calculus with Theory Spring 2011 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms ....
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MIT18_024S11_Pset3 - take any derivatives). You can justify...

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