Help whit a problem. (I have no idea)

1. Dec 3, 2004

mprm86

Calculate $e^A$ if $A = \left(\begin{array}{cc}0 & -2\\1 & 3\end{array}\right)$

Maybe using that $$e^x = \sum_{n=0}^\infty \frac{x^n}{n!}$$, then

$$e^A = \sum_{n=0}^\infty \frac{\left(\begin{array}{cc}0 & -2\\1 & 3\end{array}\right)^n}{n!}$$
but i dont know if this is the right way for doing this. Please help me. Thanks.

2. Dec 3, 2004

AKG

That's precisely it.

3. Dec 3, 2004

Ok, thanks.

4. Dec 4, 2004

HallsofIvy

Staff Emeritus
Although you may have difficulty calculating $$\left(\begin{array}{cc}0 & -2\\1 & 3\end{array}\right)^n$$
Knowing that its eigenvalues are 1 and 2 (with eigenvectors <2, -1> and <1, -1> respectively) will help.