Solved: In 39 and 40, the matrices are A(t) and B(t) are

Chapter 9, Problem 40E

(choose chapter or problem)

In Problems 39 and 40, the matrices $A(t) \text { and } B(t)$ are given. Find

$\int A(t) d t$

(b) $\int_{0}^{1} B(t) d t$

$A(t)=\left[\begin{array}{ll} 1 & e^{-2 t} \\ 3 & e^{-2 t} \end{array}\right]$

$B(t)=\left[\begin{array}{cc} e^{-t} & e^{-t} \\ -e^{-t} & 3 e^{-t} \end{array}\right]$

Equation Transcription:

$A(t)\ and\ B(t)$

$\int\limits_{\ }^{\ }A(t)\ dt$

$\int\limits_{0}^{1}B(t)\ dt$

$\frac{d}{dt}[A(t)B(t)]$

$A(t)=$ [ ${\ }_{\ 3\ \ \ {\ \ e}^{-2t}\ }^{\ 1\ \ \ \ {\ e}^{-2t}\ }$ ]

$B(t)=$ [ ${\ }_{\ {\ -e}^{-t}\ \ \ \ \ \ {3e}^{-t}\ }^{\ \ {\ \ \ e}^{-t}\ \ \ \ \ {\ e}^{-t}\ }$ ]

Text Transcription:

A(t) and B(t)

\int A(t) dt

\int 01B(t) dt

ddt[A(t)B(t)]

A(t)=[ 3 e-2t 1 e-2t ]

B(t)=[ -e-t 3e-t e-t e-t ]

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