MATH 312 Midterm: MATH 312 UPenn 312S13Exam 2
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Part a has shorter 5 questions, (10 points each so total 50 points) while part b had 5 problems (15 points each, so total is 75 points). Closed book, no calculators or computers but you may use one 3 5 card with notes on both sides. Part a: five short answer questions (10 points each, so 50 points). Let a be a 5 5 real matrix with det a = 1. We consider the equation ax = b where x and b are in r4 and a is a. A matrix is nilpotent if ak = 0 for some positive integer k [example: (cid:18)0 1. If is an eigenvalue of a nilpotent matrix, show that = 0 [suggestion: begin with. In r4 , nd the distance from the point (1, 2, 0, 3) to the plane x1 + 3x2 x3 + x4 = 0.
