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[Q243) Solve the initial value problem z' = Aš, ž(0)=(0,0,-7), where A is the 3x3 matrix...
(a) Solve the initial value problem 2" +2r' + r = 8(t - 2), z(0)=1, 2'0) = 2 (b) Consider the initial value problem -2 -5 z(0) = 3 Find ö(t), writing your answer as a single vector. k 2 k 0 1] (c) Consider the matrix 0 -2 k 3 i. Compute the determinant. ii. For what value(s) of k does A exist? iii. For what value(s) of k does the linear system A7 = 7 have nontrivial solutions?...
Let A = ( a1 0 ... 0 0 a2 ... 0 ... ... ... 0 0 an) be an n * n matrix, where a1, a2, . . . , an are nonzero real numbers. (a) Find the general solution to the system of equations -> -> x' = A * x (b) Solve the initial value problem x1(0) = x2(0) = · · · = xn(0) = k, for some constant k. (c) Solve the initial value problem (x1(0) x2(0)...
A 3x3 matrix A has eigenvalues 1 + 21,1 - 2i, and 3. Which one of the following could be A? 6 A= 1 0 1 0 6 3 -1 1 O 0 3 -1 A= 3 -1 – 4 0 1 2 1 A= -2 1 20 0 8 4 -1 O A= 1 -4 21 0 30 -2 5 1 о 3 2 0 A= 2 1 -4 -4 -1 0
Problem 9 6.3, Exercise 7. Solve the initial value problem where r(0)-1 and y(0)-2
2. Use the Laplace Transform to solve the initial value problem y"-3y'+2y=h(t), y(O)=0, y'(0)=0, where h (t) = { 0,0<t<4 2, t>4
alue problem yn value) +13y=0, y(0)=3.y (0)-Owe use the To solve an initial v eigenvalue method. (Complex eigenvalue 1. I) Convert the equation into a first order linear system 2) Write the system in the matrix form: 3) Find the eigenvalues: 4) Find associated eigenvector(s): 5) Write the general solution of the system figure out the c and c2 To find the particular soluion 6) 2 7) Find the particular solution of the system 8) Write the particular solution of...
# 2 please In Exercises 1-20 solve the initial value problem. Where indicated by CIG-graph the solution. 1. y" + 3y' + 2y = 6e21 + 28(1 - 1), y(0) = 2, y'(0) = -6 2. C/G Y" + y' – 2y = -106-' +58(1 - 1), y(0) = 7, y'(0) = -9 3. y" - 4y = 2e-' +58(1 - 1), y(0) = -1, y' (O) = 2 4. CIG y" + y = sin 3t + 28(t –...
(1 point) Consider the Initial Value Problem xi(0) 6 = 10xi-4x2 (a) Find the eigenvalues and eigenvectors for the coefficient matrix. ,V2- and 12 (b) Solve the initial value problem. Give your solution in real form x1F X2= (1 point) Consider the Initial Value Problem xi(0) 6 = 10xi-4x2 (a) Find the eigenvalues and eigenvectors for the coefficient matrix. ,V2- and 12 (b) Solve the initial value problem. Give your solution in real form x1F X2=
Use matrix techniques to solve the initial value problem -6 2. X' X X(0) = 18 -3 1
Solve the given initial-value problem. Solve the given initial-value problem. 1 X' = 0 0 1 0 1 0 X, X(0) = 1 0 0 6 7 X(t)