The matrix is
$$ A = \begin{pmatrix} 4 & -2& \\ 3 & -1&\\ \end{pmatrix} $$
And I need to caluclate $\exp(At)$, where $t$ is real.
Not sure what I need to do after I multiply everything by $t$
please help :)
The matrix is
$$ A = \begin{pmatrix} 4 & -2& \\ 3 & -1&\\ \end{pmatrix} $$
And I need to caluclate $\exp(At)$, where $t$ is real.
Not sure what I need to do after I multiply everything by $t$
please help :)
Hint
Diagonalize $At$, which will give you $P$ such that $At=PDP^{-1}$.
Remark that if $\exp(At)=P\exp(D)P^{-1}$.
Since $D$ is diagonal, $\exp(D)$ is easy to calculate.
You can use the Laplace transform; $$\exp(At)=\mathscr{L}^{-1}\{ (sI-A)^{-1} \}.$$