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(a) If X(t) = ( x11(t) x12(t) x21(t) x22(t) ) and u(t) =

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(a) If X(t) = ( x11(t) x12(t) x21(t) x22(t) ) and u(t) = ( u1(t) u2(t) ) , show that (Xu) ? = X? u + Xu? . (b) Assuming

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(a) If X(t) = ( x11(t) x12(t) x21(t) x22(t) ) and u(t) = ( u1(t) u2(t) ) , show that (Xu) ? = X? u + Xu? . (b) Assuming that X(t) is a fundamental matrix for x? = P(t)x and that u(t) = ? X?1(t)g(t) dt, use the result of part (a) to verify that xp(t) given by Eq. (15) satisfies Eq. (1), x? = P(t)x + g(t). In each of Problems 2 through 5, use the method of variation of parameters to find a particular solution using the given fundamental set of solutions {x1, x2}.

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