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Let P be an invertible matrix and assume that A = PMP[itex]^{-1}[/itex]. Where M is

M = [{3,1,0}{0,3,0}{0,0,2}]

Find a matrix B(t) such that e[itex]^{tA}[/itex] = PB(t)P[itex]^{-1}[/itex].

Now this might be an easy problem, but I really have no idea what to do because my lecturer is so bad and the book for the course doesn't cover this material.

I have seen something about A= PBP[itex]^{-1}[/itex] implying e[itex]^{tA}[/itex] = Pe[itex]^{tB}[/itex]P[itex]^{-1}[/itex] so I have tried computing the exponential of M, but to no avail. Any advice is much appreciated.