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Name + Uffi: D ‘tn’5 C.Wei Section (circle one): S.Bagley Math 2250-4 Super Quiz 2 November 1, 2013 1 a) What is the of a collection of vectors v , 1 2’ v? .L (1 point) , , 1 lb) What does it mean for vectors v 2’ ... v to be linearly independent? (1 point) () 1 c) What is a basis for a vector space/subspace W? (1 pornt) 2a) Find a basis for the solution space to homogeneous matrix equation A the left below, and its reduced row echelon form is on the right. 2 6 0 0 0 3 -6 1 4 F 67Q 9 -8 -25 5 -3 1(i) IO = , where A is the matrix on 1 3 0 -3 010 001 U 1 O 2 0 0 0 0 1 ooj 116j0 (6 points) F_\ 0 :t xl ( 1-3 2 ,c \\x - 43b -b I I LJ L I j Q o L°i I i LJ 2b) What is the dimension of the solution space in part 2a? (1 point) 3) Consider the differential equation below for a function x(t), which could arise from an unforced massspring configuration: x’’(t) +2x’(t) + lOx(t)=0. 3a) Find tlgieral solutiontd this homogeneous linear differential equation. Hint: use the characteristic polynomial method to ffit fmd a basis. (6points) o —o (-) 2 (r--ñ r9Q z -‘ 3b) ‘Which of the three damping phenomena is exhibited by solutions to this differential equation? (1 point) I’— p(rJ . 3c) Now consider the inhomogeneous DE x’ (1) + 2 x’ (1) + 10 x(t) -20. =—2 is a particular solution. Use this fact and your previous work to write down the general solution to the inhornogeneous DE. (2 points) 2 Notice that 3d) Solve the initial value problem x’’(t) +2x’(t) + lOx(1)-20 x(0) = 1 x’ (0) = 3. (6 points) + ( c3 tt) )L’(oz3 3 -3 ) cz