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

1/25/2017 Homework #1 • It must be completed on-line in McGraw Hill Connect. • Accessible after 5:00 p.m., January 26. • Closes at noon, February 7. • No deadline extension is allowed. • No discussion on the homework questions is allowed. • Chapters 1 through 3 covered. • Ten multiple-choice questions,10 points each. • You are allowed to re-do and re-submit it until the closing date. • Every time you submit it, you can find out what your total score is. • On-line signing up for Connect will close on January 31. GEOL 1303-003, Spring 2017 1 Igneous Rocks, Intrusive Activity, and the Origin of Igneous Rocks Physical Geology 15/e,