(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A=[tex]\begin{bmatrix}-1 & 2 & 0\\-2 & -1 & 0\\ 0 & 0 & -3\end{bmatrix}[/tex]

Use matrix A and compute exp(tA) explicitly.

2. Relevant equations

I am having trouble figuring out how to start this. I know how to look at each component of matrix A and to use exp(tA)=I+tA +.....(exponential expansion) but I am not sure how to simplify each component's expansion. I don't know if there is an easier way to break matrix A up? Please help me to get started!

3.I have noticed that this matrix A is in canonical form with complex eigenvalues and 1 distinct eigenvalue -3. I tried to break this matrix up into 2 matrices (B and C) that commute so that exp(A)=exp(B)exp(C), but matrix C is a nilpotent matrix with all 0's except -3(bottom right corner) and matrix B has an alpha-beta block in the upper right left corner....

The attempt at a solution

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# Matrix exponential

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