questions below:

Find a fundamental matrix for the system x'(t) = Ax(t) for the given matrix A. -3 A = - 3 6 3 Choose the correct fundamental matrix below. e 3t O A. X(t) = 0 - p 3t -te 3t O B. X(t) = cos 3te t sin 3te t (- cos 3t + sin 3t) e' (- sin 3t - cos 3t) e O c. X(t) = cos 3t sin 3t - cos 3t + sin 3t - sin 3t - cos 3t e 3t O O D. X(t) = 3t - e - 3tDetermine whether the given vector functions are linearly dependent or linearly independent on the interval ( - co, co). [ ] [2] . . . Let x1 = 4 |and x2 - Select the correct choice below, and fill in the answer box to complete your choice. O A. The vector functions are linearly dependent since there exists at least one point t in ( - co,co) where det x, (t) x2(t)] is 0. In fact, det [x, (t) x2 (t)] =. O B. The vector functions are linearly independent since there exists at least one point t in ( - co,co) where det x, (t) X2(t)] is not 0. In fact, det x, (t) x2 (t) ] = O C. The vector functions are linearly independent since there exists at least one point t in ( - co,co) where det x, (t) X2(t)] is 0. In fact, det[x, (t) x2(t)] =. O D. The vector functions are linearly dependent since there exists at least one point t in ( - co,co) where det x, (t) X2(t) ] is not 0. In fact, det x, (t) x2 (t)] =