Question: Q1 Let AcMg (IR) be a 9x2 matrix with eigenvalues a) If 2. 7 29 , then Agt Art exp (tA ) = - age

Let AcMg (IR) be a 9x2 matrix with eigenvalues a) If 2. 7 29 , then Agt Art exp (tA ) = - age It edit _ past A 6) If A . = 2 2 = 1 , then exp (tA ) = eat ( 1 - at)Itte at PFind all 2 X 2 matrices A E M203.) that satisfy the following \"crazy\" property: exp(tA) = I + M, W 6 1a (5) Give a detailed argument nding all such matrices that also establishes that you found all of them. (Hint: Can such a matrix have eigenvalues A1 7E A2? What about if A1 = A2 = X?)

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