PROBLEM 3. Suppose that the general solution of a 2-by-2 system x' = Ax is x(t)...
Problem 6 (3 points) The general solution of the system of the linear system * = AY, Y)= ((0),y(t)), is given below. (1) Sketch the strait- line solutions and the phase portrait. DO NOT forget to use ARROWS. Make sure that your sketch shows ABSOLUTELY CLEAR slopes of Tangent line as t oot -oo. (2) Is the solution stable? Y(t) = kV1 + kye" V2; V. =(2,-1), V, = (1,3)
Suppose 7' = AT, where A is the 2 x 2 matrix below. A= (1 1 1 3 (a) Determine the eigenvalues and eigenvectors of A. (b) Express the general solution of t' = Az in terms of real valued functions. (c) Sketch the phase portrait of the system. Do not forget to label your axes.
Find a general solution of the system x'(t) = Ax(t) for the given matrix A. x(t) = _______
Find a general solution of the system x' (t) = Ax(t) for the given matrix A.
Find a general solution of the system x'(t) = Ax(t) for the given matrix A. 12 51 A= -3 - 12
Find a general solution of the system x' (t) = Ax(t) for the given matrix A. 3 -- 1 A= 10 -3 x(t) = 0 (Use parentheses to clearly denote the argument of each function.)
Find a general solution of the system x'(t) = Ax(t) for the given matrix A. 8 2 A=1 34 - 8 x(t)= (Use parentheses to clearly denote the argument of each function.)
2) Sketch the phase portrait of the system x' (t) = Ax (t) if (a) 5= [ 9), P=[7"}] (1) 5= [ • ? ], P=[} >>]
Consider the matrix A. A = Write the general solution of the system x'(t) = Ax(t) in the form x(t) = C,x,(t) + Cox,(t). Enter any column vector xce) = cze-34–1,1) + cze +36(84–1,1)+(-1,0))
Find a general solution of the system x'(t) = Ax(t) for the given matrix A. - 20 15 15 A= 7 7 - 4 - 23 - - 15 18 x(t) = (Use parentheses to clearly denote the argument of each function.)