E^A matrix power series (eigen values, diagonalizable)

[Fellowroot]

Homework Statement

Find an expression for e^A with the powerseries shown in the image linked

Homework Equations

I know you have to use eigen values and eigen vectors and a diagonal matrix

The Attempt at a Solution

What I did was just try to actually multiply out the infinite series given. I took it out to about 3 terms and said on my quiz that the rest will eventually go to zero so that this series will converge. However I got zero credit for this solution.

I know how to get eigen values, but I just need help finding out how to get Q.

Thanks.

 

[micromass]

Can you find the eigenvectors? Those will typically be the columns of $Q$.