This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: 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 R 1 1 p ( x ) dx = 0. e) The set of solutions y = y ( t ) of y 00 + 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....
View
Full
Document
This note was uploaded on 03/06/2012 for the course MATH 260 taught by Professor Staff during the Spring '12 term at UPenn.
 Spring '12
 STAFF
 Math

Click to edit the document details