question below:

Find a fundamental matrix for the system x'(t) = Ax(t) for the given matrix A. - 2 2 A= -4 2 . . . Choose the correct fundamental matrix below. O A. X(1) = cos 2t sin 2t cos 2t - sin 2t sin 2t + cos 2t e 2t 0 O B. X(t) = e 2t + 2t e 2t O c. X(t) = 0 e2t e - 2t O D. X(1) = cos 2te t sin 2t e t ( cos 2t - sin 2t) e ( sin 2t + cos 2t) etUse Euler's method with step size h = 0.2 to approximate the solution to the initial value problem at the points x = 5.2, 5.4, 5.6, and 5.8. 3 y'=;(y2+y),y(5)=3 Complete the table using Eulel's method. n X" Euler's Method 1 5.2 _ 2 5.4 _ 3 5.6 4 5.8 (Round to two decimal places as needed.)