Kindly solve all the problem there in the attached photo. Thank you! In class, w

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Kindly solve all the problem there in the attached photo. Thank you!

In class, we defined eA = infinity n = 0 An/n!, and showed that x(t) = eAtc is a solution to the IVP ' = A , (0) = . We say that the matrix A is a diagonal matrix if the only nonzero entries arc 011 the diagonal, like so: Determine eA where A is the displayed diagonal matrix. Two matrices A and B arc conjugate (also called similar) if there is an invertible matrix X such that A = XBX-1 Show that if A = XBX-1 then An = XBnX-1 Show that if A = XBX-1 then eA = XeBX-1. Evaluate (I'm writing exp(A) for eA.) Write down the solution to the IVP

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