Consider the initial value problem d dix(t) where xo is some constant vector. = A(t)x(t) +...

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Consider the initial value problem d dix(t) where xo is some constant vector. = A(t)x(t) + f(t), x(0) = xo (a) Assuming (A(r)dr) A(t) = A(t) ([ A(-)dr). Show that the matrix X(t) = elő Arian satisfies the matrix differential equation: X(t)= A(t)X(t). di (b) Obtain a solution to the initial value problem, given A= - (-₁3), f(t)=e¹ (-¹1), x(0) = (b). Consider the initial value problem d dix(t) where xo is some constant vector. = A(t)x(t) + f(t), x(0) = xo (a) Assuming (A(r)dr) A(t) = A(t) ([ A(-)dr). Show that the matrix X(t) = elő Arian satisfies the matrix differential equation: X(t)= A(t)X(t). di (b) Obtain a solution to the initial value problem, given A= - (-₁3), f(t)=e¹ (-¹1), x(0) = (b).