Math 2243 Practice Final Fall 2005 Instructors S Joo M Kurzke Name Discussion Session 021 Javier Zuniga TTh 10 10 022 Chung I Ho TTh 10 10 023 Javier Zuniga TTh 11 15 024 Chung I Ho TTh 11 15 031 Doyoon Kim TTh 2 30 032 Javier Zuniga TTh 2 30 033 Doyoon Kim TTh 3 35 Exam time Thursday Dec 15 1 30 4 30 13 30 16 30 Exam location 021 Ford Hall B10 022 Ford Hall B15 023 Ford Hall B29 024 Ford Hall B80 031 Ford Hall 110 032 Ford Hall 115 033 Ford Hall 127 Exam Rules One line scientific calculators are allowed No books or notes All questions are partial credit Put final answers in boxes where appropriate Good Luck You will need your student ID for the real final Finals without a student ID can not be accepted 1 25 pts 1 Determine whether or not the set S 5et 3t2 et t2 et is linearly independent on Is 2t2 4t in the span of S Justify your answer 1 25 pts 2 Find the general solution of y 00 3y 0 2y et 2 25 pts 3 The number of bacteria in a colony increases at a rate proportional to the number present If the number of bacteria doubles in 5 hours how long will it take this colony to grow to seven times its original size 3 20 pts 4 Solve the initial value problem y 0 t2 y 2 1 4 y 0 0 30 pts 5 Find the general solution of 0 x 4 3 2 x 3 4 7 5 25 pts 6 Are these sets V A M22 A AT and W A M22 det A 0 subspaces of M22 Justify your answer 6 25 pts 7 Solve the initial value problem 1 0 y y t2 t 7 y 0 5 30 pts 8 Find the general solution of the system 1 2 0 x0 6 5 0 x 2 3 5 8 25 pts 9 Compute the determinant and the inverse of the matrix 2 3 5 1 3 A 0 1 1 2 9 15 pts 10 Find the general solution for the differential equation y 0 2ty 3t 10 30 pts 11 Convert the equation y 00 5 sin y 0 y 2 y 0 to a corresponding system and determine the location type and stability of all equilibrium points via the linearization of that system at its equilibrium points system equilibrium points types and stability 11 25 pts 12 Determine the kernel the nullity and the given by 5 T v 6 7 12 rank of the transformation T R4 R3 3 0 1 4 0 2 v 7 0 7