Chapter B, Problem 29E

(a)

To determine

The value of $\frac{dA}{dt}$ for the matrix $A\left(t\right)=\left[\begin{array}{cc}{e}^{4t}& \cos \pi t\\ 2t& 3t^2-1\end{array}\right]$.

(b)

To determine

The value of ${\displaystyle \underset{0}{\overset{2}{\int }}A}\left(t\right)dt$ for the matrix $A\left(t\right)=\left[\begin{array}{cc}{e}^{4t}& \cos \pi t\\ 2t& 3t^2-1\end{array}\right]$.

(c)

To determine

The value of ${\displaystyle \underset{0}{\overset{t}{\int }}A}\left(s\right)ds$ for the matrix $A\left(t\right)=\left[\begin{array}{cc}{e}^{4t}& \cos \pi t\\ 2t& 3t^2-1\end{array}\right]$.