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(Solved): matrix derivativesolve part c please  Let \( A(t)=\left[\begin{array}{rr}5 t & e^{t} \\ 3 & 7 e ...



matrix derivative
solve part c please 


Let \( A(t)=\left[\begin{array}{rr}5 t & e^{t} \\ 3 & 7 e^{t}\end{array}\right] \) and \( B(t)=\left[\begin{array}{rr}7 \cos
Let \( A(t)=\left[\begin{array}{rr}5 t & e^{t} \\ 3 & 7 e^{t}\end{array}\right] \) and \( B(t)=\left[\begin{array}{rr}7 \cos t & -9 \sin t \\ 5 \sin t & \cos t\end{array}\right] \). (a) Find \( \int \mathbf{A}(t) \mathrm{dt} \). (b) Find \( \int_{0}^{1} B(t) d t \) (c) Find \( \frac{d}{d t}(A(t) B(t)) \). (a) \( \int \mathbf{A}(\mathrm{t}) \mathrm{dt}=\left[\begin{array}{ll}\frac{5 t^{2}}{2}+\mathrm{c}_{1} & e^{t}+\mathrm{c}_{2} \\ 3 \mathrm{t}+\mathrm{c}_{3} & 7 e^{t}+\mathrm{c}_{4}\end{array}\right] \) (Type an exact answer.) (b) \( \int_{0}^{1} B(t) d t=\left[\begin{array}{rr}7(\sin 1-\sin 0) & 9(\cos 1-\cos 0) \\ -5(\cos 1-\cos 0) & \sin 1-\sin 0\end{array}\right] \) (Type an exact answer.) (c) \( \frac{d}{d t}(\mathbf{A}(t) \mathbf{B}(\mathrm{t}))= \) (Type an exact answer.)


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