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# hw1 - Math 260 Spring 2012 Jerry L Kazdan Problem Set 1 Due...

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Math 260, Spring 2012 Jerry L. Kazdan Problem Set 1 Due: In class Thursday, Jan. 19. Late papers will be accepted until 1:00 PM Friday . These problems are intended to be straightforward with not much computation. 1. At noon the minute and hour hands of a clock coincide. a) What in the first time, T 1 , when they are perpendicular? b) What is the next time, T 2 , when they again coincide? 2. Which of the following sets are linear spaces? a) { X = ( x 1 , x 2 , x 3 ) in R 3 with the property x 1 - 2 x 3 = 0 } b) The set of solutions x of Ax = 0, where A is an m × n matrix. c) The set of 2 × 2 matrices A with det( A ) = 0. d) The set of polynomials p ( x ) with 1 - 1 p ( x ) dx = 0. e) The set of solutions y = y ( t ) of y + 4 y + y = 0. [ Note: You are not being asked to solve this differential equation. You are only being asked a more primitive question.] 3. Consider the system of equations x + y - z = a x - y + 2 z = b 3 x + y = c a) Find the general solution of the homogeneous equation. b) If a = 1, b = 2, and c = 4, then a particular solution of the inhomogeneous equa- tions is x = 1 , y = 1 , z = 1. Find the most general solution of these inhomogeneous equations.

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hw1 - Math 260 Spring 2012 Jerry L Kazdan Problem Set 1 Due...

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