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Question: 2 sometimes matrices appear as the argument of a transcendental...

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2. Sometimes matrices appear as the argument of a transcendental function. Let M be defined as -1 Let xe R. We can calculate A -eM as follows: (a) Compute M. M and M b) From the results of (a), infer what M must be for any positive integer n. c) Write out the Taylor series expansion for e; ie 23 4 2 34 d) SubstitutexM into the above Taylor series and carry out the appropriate operations. Replace the first term, i, by the 2 2 identity matrix . Note thatA erM İs a matrix! e) Write out the first few terms for each element of A. (f) Do you recognize the resulting series for each element? If so, replace the infinite sum in each element by its function (g What are the entries in the matrix A when x/2?

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