Problem 4. Given a scalar a, the exponential e" can be expanded by Taylor series as: 1 1 1 2 3 4 e = 1+a+ a + a + ·a +... 2! 3! 4! Similarly, we define the matrix exponential e of any n x n matrix A as 1 1 1 e I + A+ A²+ 2! If A is diagonalizable to a diagonal matrix D, (a) Expressed by e (b) 1 1 1 1 0 012 Compute e for A= 0 A³ + 3! 4! +...

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