please label answers clearly Assume that a 2 x 2 matrix A has eigenpairs X ati,...
Please help Find the solution to the initial value problem: x(0)-0x(O)--1 x(t) write x(t) as a product of a sine and a cosine, one with the beat (slow) frequency (μ-2)/2 , and the other with the carrier (fast) frequency (μ+ 2)/2 x(t) The solution x(t) is really a function of two variables t and μ . Compute the limit of x(t씨 as μ approaches 2 (your answer should be a function of t. lim x(t,H) Define y(t)-lim x(t,u) What differential...
Please do parts (a), (b), and (c). Please write clearly and be neat! Problem 1 Find a fundamental solution set B and the corresponding set of solutions S for the system AX(t)-X), where 0 2 7 A=1207 7 2 0 (a) First, find e-values and e-vectors for A. (b) Write down B and S. (c) Is A diagonalizable? If so, give the details (write down the diagonal transformatiorn BAC = D, explaining exactly what B, C, and D are) and...
(7 10 Two connected tanks, each with a capacity of 60 liters, contain brine (salt water) Initially the firs tank contains 40 liters and the second tank contains 30 liers. Brine with a salt conccntration of 1 grams per litcr flows into the first tank at S litcrs per hour. Well-stirred brine flows from the first tank into the second at 7 liters per hour from the second nto the fist at3 lters per honr, from the first into a...