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

Chapter 10, Problem 10.2

(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 = 2x1 + x2, x 2 = 3x1 + 6x2, x1(t)= c1e4t cos(t) + c2e4t sin(t) x2(t)= 2c1e4t [cos(t) sin(t)] +2c2e4t [cos(t) + sin(t)], x1(0)= 2, x2(0) = 1