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Find e^A Using the Taylor Series.

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HI Professor Shafrir, I have chosen you because I like your pedagogic method for explaining each steps.
In the following attached problem, the professor gives us the solution but didn't explain the way.

So I don't need the solution, I have it. All I need to understand is how to get from step 1 (the Taylor series) to step 2 (The last step) with a matrixe e^A with entries consisting in exponentials e, for questions (a) and question (b) only.

Thank you, Professor.

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The expert finds e^A using the Taylor Series.

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Hello and thank you for posting your question to Brainmass.
The solution is attached below in two files. the files are identical in content, only differ in format. The first is in MS Word format, while the other is in Adobe pdf format. Therefore you can choose the format that is most suitable to you.

The Taylor series expansion of about is given by:
...

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