2005Fall20MTIII-sol

# 2005Fall20MTIII-sol - Name ID Solutions to Midterm III Math...

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Name: ID#: Solutions to Midterm III Math 20 Introduction to Linear Algebra and Multivariable Calculus December 16, 2005 Rules: This is a one-hour exam. Calculators are not allowed. Unless otherwise stated, show all of your work. Full credit may not be given for an answer alone. You may use the backs of the pages or the extra pages for scratch work. Do not unstaple or remove pages as they can be lost in the grading process. Please do not put your name on any page besides the first page. If you like, you may put your ID number on the top of each page you write on. Hints: Read the entire exam to scan for obvious typos or questions you might have. Budget your time so that you don’t run out. Problems may stretch across several pages. Relax and do well! Students who, for whatever reason, submit work not their own will ordinarily be required to withdraw from the College. —Handbook for Students

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1 1 1. (5 Points) Let T : R 2 R 2 be the linear transformation whose standard matrix is A = [ T ] E = 2 8 4 - 2 Let B = 1 1 , 1 - 1 Find [ T ] B . Solution. Let P be the matrix whose columns are the elements of B in the coordinates of E . That is, P = 1 1 1 - 1 . Then [ T ] B = P - 1 AP = 1 2 1 1 1 - 1 2 8 4 - 2 1 1 1 - 1 = 6 0 4 - 6 . / 5 1
2 2 2. (5 Points) It is March 1943, and Rear Admiral Kimura Masatomi is trying to move a convoy from Rabaul, on the northeastern tip of the island of New Britain, to Lae, just west of New Britain on the island of New Guinea.

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