Find a fundamental matrix of the following system, and then apply x(t) = (t)P(0) 'x, to find a solution satisfying the initial conditions. - 6 - 5 x, x(0) = 6 36 1 Find a fundamental matrix for the given system. Select the correct answer below. - 5 sin 12t - 6 cos 12t + 12 sin 12t 12 cos 12t + 6 sin 12t 5 cos 12t 'A. $(t) = 6 + 5t - 12t 2 -5 e O B. P(t) = 2 + 5t - 6-5 e - 12t 6 cos 12t 5 sin 6t – 5 cos 12t O c. D(t) =| 5 sin 6t + 12 cos 12t - 6 sin 12t - 12t 6 e - 12t - 5 e O(t) = 12t 12t - 5 e 6 e Find a solution satisfying the given initial condition. X(t) = (Use integers or fractions for any numbers in the expression.)

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