matrix exponential

[logistic_guy]

\(\displaystyle \textcolor{indigo}{\bold{Solve.}}\)

\(\displaystyle \bold{A} = \begin{pmatrix} 2 & 0 \\ 0 & 3 \end{pmatrix}\)

 

[logistic_guy]

The question wants us to find \(\displaystyle e^{\bold{A}t}\) when \(\displaystyle \bold{A} = \begin{pmatrix} 2 & 0 \\ 0 & 3 \end{pmatrix}\).

\(\displaystyle \textcolor{indigo}{\bold{Beautiful}}\), but \(\displaystyle \textcolor{red}{\bold{not}}\) \(\displaystyle \textcolor{black}{\bold{easy}}\)!

 

[logistic_guy]

\(\displaystyle \bold{A}^2 = \begin{pmatrix} 2^2 & 0 \\ 0 & 3^2 \end{pmatrix}\)

 

[logistic_guy]

\(\displaystyle \bold{A}^3 = \begin{pmatrix} 2^3 & 0 \\ 0 & 3^3 \end{pmatrix}\)