Solved: In each of 1 through 5, (a) verify that the given functions satisfy the system

Chapter 10, Problem 10.3

(choose chapter or problem)

In each of 1 through 5, (a) verify that the given functions satisfy the system, (b) write the system in matrix form X= AX for an appropriate A, (c) write n linearly independent n 1 matrix solutions 1, , n , for appropriate n, (d) use the determinant test of Theorem 10.2(2) to verify that these solutions are linearly independent, (e) form a fundamental matrix for the system, and (f) use the fundamental matrix to solve the initial value problemx 1 = 3x1 + 8x2, x 2 = x1 x2, x1(t)= 4c1e(1+2 3)t + 4c2e(12 3t) , x2(t)= (1 + 3)c1e(1+ 3)t + (1 3)c2e(12 3)6t , x1(0)= 2, x2(0) = 2